Thanks to Glen W. of Texas for sending me the link to this video clip. It involves a Russian paraglider pilot and an eagle over the Himalayas. They collide in mid-air, shown about 30 seconds into the video clip, followed by the pilot deploying his emergency parachute and descending safely to a heavily-wooded hilltop below. The rest of the video shows his attempts to disentangle himself and free the eagle from the strings and straps of his paraglider (which he manages to do successfully - skip forward to about the 9 minute mark to see the final stages of the process, and watch the eagle fly away, seemingly uninjured).
I bet that's one flight the pilot will never forget! Judging from the number of beeps in the recording, he must have used more than a few Russian words that are best left untranslated . . .