The narrator starts by lamenting that he does not know love himself. One day, while reading a book about a prophetic dream (Cicero's "Dream of Scipio"), he falls asleep and has his own dream in which the Roman general Scipio appears and leads him up through the celestial spheres to the temple of Venus, decorated with images of doomed lovers.
Passing through, they come to a garden where he sees Cupid making arrows, as well as several other allegorical figures connected to the quest for love (Pleasure, Adornment, Lust, Courtesy, Cunning). Here the personification of Nature is holding a parliament in which birds will choose their mates. Three male eagles try to make their cases for who should mate with the sole female eagle.
There is no conclusive winner in this debate. The other birds are getting restless, waiting for the eagles to finish, and want to lave. The turtledove tells them to wait and let the eagles' debate play out. Nature decides to speed things up by selecting a judge.
The male falcon is selected to judge the eagles' situation, and suggests (in chivalric-tournament style) a battle between the three. The goose speaks up and suggests that maybe the female eagle should be given the choice herself. The female eagle says she cannot make a decision, and would like another year to think about it. Nature agrees, and tells the males to stay faithful while waiting.
After this, all the other birds pair off and began to chatter and sing. The noise wakes up the narrator, who resumes reading.
The poem is 700 lines, but one line has been quoted in more scholarly (and mundane) periodicals than any other, and that is line 309-10:
For this was on Seynt Valentynes day,Whan every foul cometh ther to [choose] his [mate],
...and again, starting at line 319:
This noble emperesse, ful of grace,Bad every foul to take his owne place,As they were wont alwey fro yeer to yere,Seynt Valentynes day, to [stand] there.
This is the earliest known reference to St. Valentine's Day being connected to the idea of love or choosing a mate. It may simply be that 14 February was warm enough that birds started being more active and building nests. There was a Medieval Warm Period when average temperatures were higher than they were after 1400, so mid-February might not be too great a stretch for spring activity.
Whatever the reason in Chaucer's mind, it gives us a reason to turn to St. Valentine, and get at the heart (pun intended) of this legend.