Yes, Chaucer knew Dante's works very well, and borrows from him liberally. For one of the longer examples, the story of Erl Hugelyn in the Monk's Tale is the story of Count Ugolino from Canto XXXIII of the Inferno, and Chaucer even cites his source:

Whoso wol here it in a lenger wise

Redeth the grete poete of Ytaille

That highte Dant, for he kan al devyse

Fro point to point, nat o word wol he faille.

Whoever wants to hear it in a longer version

Read the great poet of Italy

Who is called Dante, for he can all narrate

In great detail; not one word will he lack.

(Translation from https://sites.fas.harvard.edu/~chaucer/teachslf/mkt-par.htm)

Chaucer had at least a reading knowledge of Italian, and encountered the new style of vernacular Italian poetry during his diplomatic missions to Italy. After this, he produces a number of adaptations of works by Dante, Petrarch, and Boccaccio. (Historians used to believe he knew at least Boccaccio personally, and maybe Petrarch, but now that's not considered proven. Oddly enough I don't think Chaucer ever admits his creative debt to Boccaccio by name; the closest he gets is attributing a story from Boccaccio to "Lollius".)

Sources:

• The Canterbury Tales, tr. Ronald L. Ecker and Eugene J. Crook, Hodge & Braddock, 1993 (available online at http://english.fsu.edu/canterbury/)

• Critical Insights: The Canterbury Tales, ed. Jack Lynch, Rutgers, 2010