The Consolation of Philosophy, by Anicius Manlius Severinus Boethius, written in prison while he awaited execution by Theodoric, ruler of Rome, was the most popular and influential philosophical work, especially among laymen, from the sixth to the eighteenth centuries. Chaucer translated it into English, as did King Alfred before him, and Queen Elizabeth I a couple of centuries after him. It deeply influenced Chaucer's work, especially in the Knight's Tale and Troilus and Criseyda; see the introduction to Boece in the Riverside Chaucer (pp. 395-97).
Boethius was author of a number of other popular and authoritative works, including translations and commentaries on a variety of topics. Chaucer was aware of some of these works; in the Nun's Priest's Tale, Boethius' treatise on music, De musica, is cited (VII.3294).
For good introductory materials and a complete translation, see the edition in the admirable University of Virginia e-text series. The edition is by James J. O'Donnell of the University of Pennsylvania. For brief selections of particular interest to the student of Chaucer, see the following:
Book I, Metrum 1 – Boethius bewails his miserable state.
Book II, Prosa 1 – Dame Philosophy instructs Boethius on the nature of Fortune.
Book II, Prosa 2 – The nature of Fortune; Fortune and Tragedy.
Book II, Metrum 8 – The 'Fair chain of Love.'
Book III, Metrum 12 – The story of Orpheus.
Book IV, Prosa 5, Metrum 5 – Apparent confusion of the Universe. (Conclusion of Prose 4 is quoted. Then Metrum 5.)
Book IV, Prosa 5 – Providence rules Fortune.
Book IV, Metrum 6 – Love binds the warring elements of the Universe.
Book IV, Prosa 7 – The uses of Fortune.
Book V, Prosa 6 (conclusion) – Divine Providence.
For a better modern translation of Boethius, see The Consolation of Philosophy, translated, with introduction and notes, by Richard H. Green (No. 86 in the Macmillan Library of Liberal Arts, originally published by Bobbs-Merrill). For a useful study of Chaucer's translation, see Tim William Machan, Techniques of Translation: Chaucer's Boece. Norman, OK. Pilgrim Books. 1985.