Chewbacca's Ship card reads:

When you are dealt a faceup Damage card, immediately flip it facedown (without resolving its ability.)

Determination reads:

When you are dealt a faceup Damage card with the Pilot trait, discard it immediately without resolving its effect.

So my question is, assuming faceup Damage card with Pilot trait, which takes precedence? I looked on page 20 "Breaking the Rules," and that didn't seem helpful to me. I re-read page 19, and I didn't find a clear answer there either. I looked at page 16 "Suffering Damage." No luck. Thoughts? My interpretation would be player's choice, which would be Determination, but I don't know if that is right.

The FAQ mentions something about simultaneous events occurring in the order of the controller's choosing.

Yeah, I'm guessing the first question under "General" would cover it. OK. I can go with that.

(without resolving its ability.) I believe it gets put facedown first, otherwise if you draw the injured pilot you would completely negate all of chewies text, however it says you flip it down without resolving its abiltiy

Not quite, both abilities say to do something immediately without resolving the ability, so that reasoning doesn't work.

Yeah, both are "immediately," so i think they occur simultaneously, in which case the acting player gets to choose, per the FAQ, so I'd go with player's choice.