Redeth the grete poete of Ytaille
That highte Dant, for he kan al devyse
Fro point to point; nat o word wol he faille.
(Monk's Tale, VII.2460-62)
Chaucer greatly admired Dante, whom he frequently cites and sometimes quotes in a manner that seems to show he had some parts of the Divine Comedy by heart.
The prayer to the Virgin at the beginning of the Paradiso, which Dante derived from St. Bernard, seems to have been Chaucer's favorite passage in the Divine Comedy; he quotes it in the Prioress' Tale (VII.474-80; see note in The Riverside Chaucer, p. 914) and he uses it in a purely secular sense in Tr 3 1261-67 (see note in The Riverside Chaucer, p. 1042). He adapts it for the "Invocation to the Virgin" that is part of the introduction to the Second Nun's Tale:
Dante's Letter to Can Grande contains an important explanation of the "allegorical method" of literary interpretation, which Dante apparently (the authenticity of the letter has been questioned) wanted to be used in reading his Divine Comedy, or at least the Paradiso, a copy of which he sent to Can Grande with his letter:
Chaucer also uses the account of Hugolino of Pisa (from Canto 33, 1-90 of the Inferno) in his Monk's Tale:
In the Wife of Bath's Tale, Chaucer draws upon Dante's Canzone for the old hag's discussion of true nobility:
For further information, see the Digital Dante Project at Columbia University, which is well worth exploring.
So too is the impressive Dartmouth Dante Project, which contains a wealth of materials for more advanced students.