If you read any book on the text of the bible, you will sooner or later come across a statement that the chapter divisions in our modern bibles are not ancient, but are the work of Cardinal Stephen Langton, the medieval Archbishop of Canterbury, who died in 1228 AD. I have never seen this claim referenced to primary sources, however, which means that it is hard to check.
One of the better versions of this story is in Metzger’s Early versions of the New Testament. It reads as follows:
The custom of referring to chapters when quoting from the Scriptures was rare before the twelfth century.  The development of the lecture and reportatio method, however, must have shown the convenience of such a practice. The chief difficulty to its adoption arose from the lack of one generally agreed-upon system, for several systems of chapter-division from late antiquity and the early medieval period were current. The diversity was felt most acutely at the University of Paris, where the international provenance of the student body showed most clearly the absolute need for a standardized system of capitulation, as well as a standardized canonical order of scriptural books. Uniformity was introduced amid such chaotic conditions by the Paris scholars, notably, as it appears, by Stephen Langton (d. 1228), then a doctor of the University of Paris, afterwards archbishop of Canterbury and leader of the barons in the struggle which gave birth to the Magna Carta. His system, which is substantially the one in use today, was adopted in the earliest printed editions of the Vulgate. The chapters were at first subdivided into seven portions (not paragraphs), marked in the margin by the letters a, b, c, d, c, f, g, reference being made by the chapter number and the letter under which the passage occurred. In the shorter Psalms, however, the division did not always extend to seven.
 Cf. O. Schmidt, Über verschiedene Eintheilungen der heiligen Schrift (Graz, 1892), and A. Landgraf, ‘Die Schriftzitate in der Scholastik um die Wende des 12. zum 13. Jahrh.’, Bib., xviii (1937), 74-94.
 On the diversity of earlier chapter divisions, see the tabulation of differences in P. Martin, ‘Le texte parisien de la Vulgate latine’, Mu, viii (1889),444-66, and ix (1890), 55-70, and especially the important monographs by De Bruyne, Sommaires, divisions et rubriques de la Bible latine (Namur, 1920); for a summary of part of De Bruyne’s research, see Patrick McGurk, Latin Gospel Books from A.D. 400 to A.D. 800 (Les Publications de Scriptorium, vol. v; Paris-Brussels-Amsterdam, 1961), pp. 110-21.
 For a list of 284 different sequences of scriptural books in Latin manuscripts, see Berger, Histoire de la Vulgate, pp. 331-9; and for a list of twenty different sequences of the Pauline Epistles in Greek, Latin, and Coptic manuscripts, see H. J. Frede, Vetus Latina, xxiv/2, 4te Lieferung (Freiburg, 1969), pp. 290-303, and id., ‘Die Ordnung der Paulusbricfe’, Studia Evangelica, vi, ed. by E. A. Livingstone (TU cxii; Berlin, 1973), pp. 122-7.
 On the ambiguous evidence supporting the attribution to Langton, see Beryl Smalley, The Study of the Bible in the Middle Ages, 2nd edn. (New York, 1952), pp. 222-4.
The absence of primary sources in this bibliography may be noted.
Recently I was reading Diana Albino’s article on chapter divisions and chapter titles in ancient texts and found some interesting statements:
The modern division into chapters of the books of the Bible was carried out in the West by Cardinal Stephen Langton, Archbishop of Canterbury (+ 1228), rather than by Lanfranc, also Archbishop of Canterbury (+ 1089), to whom it has been erroneously attributed.
In a manuscript in the Bodleian, no. 487, probably written in 1448, we find this precise testimony: “1228: Magister Stephanus de Langueton, archiepiscopus centuariensis obiit qui biblia apud parisium quotavit.” . (I.e. “1228: Master Stephen Langton, Archbishop of Canterbury died, who divided up the bible at Paris.”)
Another witness, equally precise and also older, is that of Nicolas Trivet (1258-1328) , who wrote about Stephen Langton: “Hic super totam Bibliam postillas fecit et eam per capitula, quibus nunc utuntur moderni distinxit; ….”. (“Here he made postillas throughout the whole bible, and split it into chapters, which are now used by modern people; …”)
Otto Schmid  has collected the evidence of the manuscripts of the Bible, from which we may deduce with certainty that Stephen Langton divided the Bible into chapters.
We also know that the work was performed in 1204-1205, when he was a professor at the University of Paris . This information was obtained by Martin from manuscript 1417 of the National Library of Paris. The Langtonian division into chapters was introduced in 1226 in the edition of the Vulgate known as the Paris Bible.
 According to the lexicon of Du Cange, “quotare” means: to divide into chapters and verses.
 N. Trivet, Annales sex regum angliae, ed. A. Hall, Oxford, 1719, p. 182. [Archive.org; p.216 of the 1845 reprint]
 O. Schmid, Ueber verschieden Einteilungen der heiligen Schrift, insbesondere über die Capitel-Einteilung Stephan Langtone im XIII Jahrhunderte, Graz, 1892, p. 56-106. [Google books]
 Paulin Martin: Introduction à la critique générale de l’Ancien Testament, Paris, 1887-1888, t. II, p. 461-474.
These statements are very interesting, but for more details we need to refer to Schmid’s work, On the divisions of Holy Scripture and the chapter divisions of Stephen Langton in the 13th c.
Schmid states on p.56 that the first statement may be found on fol. 110 of Ms. Bodl. 487. On p.58 he states that it first became known to scholarship via Casimir Oudin, Comment. de scriptoribus eccles., Lips. 1772, vol. 2, col. 1702. This was repeated by later scholars.
According to Schmid, Trivet’s statement was also copied by a considerable number of scholars, whom he lists.
Schmid also has something to say about Paulin Martin’s statement. Notably the ms. is not 1447, as Albino gives it, but Ms. Paris, BNF lat. 14417. This codex is a 13th c. miscellaneous codex of 316 folios, originally from St. Victor. On f. 125v-126v there is a list of chapters of scripture. (This is followed by commentary on scripture by Langton) The list of chapters is headed, Capitula Canthuar. archiepiscopi super bibliotec. (Chapters of the archbishop of Canterbury on the bible.) Schmid then gives an edition of the chapter title list verbatim on p.59-92. He then goes on to say (p.92):
From this list it will be seen that the chapter divisions of Stephan Langton are generally the same as those contained in the Clementine Vulgate, but are not the same in terms of both number of chapters of individual sacred books, as well as with regard to the beginnings of some chapters of the same. The difference is most striking for Judith and Esther. The books Paralip., Esdras and Nehemiah are counted as one book, but otherwise the difference in the number of chapters is usually only 1. We give below a brief overview of the difference in the number of chapters, where there is one, between Langton’s division and the Clementine Vulgate. ….
We cannot decide whether Langton made and published a number of versions of his division of scripture into chapters, nor whether the version above is a later redaction of it, or the only version. However it certainly leaves us with the question of when and where he worked out the division.
Trivet (see p.56) in his report leaves it vague as to where Langton worked on his chapter division. But H. Knyghton specifies Paris explicitly; apud Parisium quotavit. This gives us a guide to determine the date. Langton was made a cardinal on 22nd June 1206 by his patron Innocent III, who had studied in Paris and probably had Langton as a colleague. This meant that Langton in 1207, when there were great disputes about the next appointment to the see of Canterbury, was elected to it in Rome.
From this he concludes that the work was done not long after 1201, probably in 1204-5, while he was teaching in Paris. Robert de Courson, also an Englishman, quotes passages of scripture using the new system in his Summa, written between 1198-1216 (since it refers to Petrus Cantor, d. 1197, and a council held in 1201, but not to the revocation of a decretal in 1216). It is extant in Ms. lat. Bibliotheque Nationale 8268, 8269 and other mss. He adds:
Denifle in his Archiv für Literatur und Kirchengeschichte, l. c., p. 291, expresses the opinion that Langton’s divisions were propagated to France and other countries through the Paris Bible, the Exemplar Parisiense (so-called by Roger Bacon), on which Denifle’s thorough investigations have shed new light. This view can only be accepted, since Paris and France in the 11th century, as in the 12th and 13th century, was the seat and centre of theological learning, where many distinguished men settled and where anyone who sought to study theology would choose to come.
The returning students, who had learned and used the new division in Paris, brought it back to their homes. Langton’s work was also disseminated by the numerous copies of the Paris bible. Sam. Berger has found confirmation of the author of the new division in ms. 340 of the town library of Lyons, in which the proverbs begin with the words, Incipiunt parabole Salomonis distincte per capitula secundum mag. Stephanum archiepis. (Here begin the parables of Solomon split into chapters according [to the system of] master Stephen the archbishop.) The divisions are also found in the Paris, Bibliotheque Mazarine ms. 29, written in 1231 AD. Certainly it will have appeared in bible manuscripts before this date.
It is not clear what inspired Langton’s work. Perhaps it was the wish of the Paris theologians to have a simpler system by which to cite the scriptures, or, as some think, the chaos of different divisions and numbers in the manuscripts caused a need for a unified system. Perhaps it was the industrious Langton’s studies on scripture – we have glosses from him on almost the whole of scripture – which led him to consider a simpler division as desirable.
Denifle, in his work, Die Universitäten des Mittelalters, Berlin 1886, and in other places, and in his Chartularium Univers. Paris., tom. I, Paris. 1889, Introd. p. VIII-X, notes that the university of Paris was born from the union of different teachers between 1200-1208, pretty much around the time when Langton was teaching in Paris and performing his division of the scripture into chapters. Possibly it was this circumstance that caused Langton to perform his work for the newly formed institution.
He continues that in the 13th century older divisions are still seen, but either the new ones are added and the old erased, or else the new ones would be added in the margin. This was so even in old manuscripts like the Codex Amiatinus, where the new divisions appear in the margins. In the new 13th c. mss. the new divisions were placed right in the text. In older mss. notes appeared in the margin: hic non notatur/signatur capitolum (here the chapter is not marked); hic non incipit cap. (here the chapter does not begin); or, secundum libros bene correctos hic debet incipit cap.( according to well-corrected mss, here the chapter should begin.) Mixed witnesses appear in some mss., such as ms. Graz c. 186. Writing a bible took time. In this case it was begun with capitulationem at the start of the book and stichometric numbers at the end, and divided according to older systems. Suddenly the new system appears, and the old Capitula, Tituli, Breves and verse numbering is omitted.
Schmid then discusses the evidence for further tweaking of the system from the manuscripts. Some books that he had treated as one were divided into two (e.g. Esdras). But the difference between the original and the Clementine Vulgate is usually only a verse or two. He says that there is still some variation, even once printing begins.
The new divisions also made their way into Hebrew mss. of the Old Testament, although only marked in the margins by Christian hands. The first printed edition of the Hebrew bible to have them was the 1523 Venice edition by Dom. Bomberg.
Greek manuscripts of the New Testament acquired these divisions only in the 15th century, especially after the fall of Constantinople, as Greeks fled to the west with their manuscripts.
Interestingly Schmid also discusses (p.108) the modern division into verses by Robert Stephanus, the printer. In the preface to his 1551 bilingual edition of the New Testament, Greek and Latin, Stephanus states:
Quod autem per quosdam ut vocant versiculos opus distinximus, id vetustissima Graeca Latinaque exemplaria secuti fecimus, eo autem libentius sumus imitati, quod hac ratione utraque translatio posset omnino e regione graeco contextui respondere.
That is, he split the work into what are called “versiculos”, because in this way anyone could cross-reference the translation and the corresponding passage of Greek.
Schmid then continues with further details of how the division into verses appeared in the early editions, but at this point we must leave him.