Okay, so it's not a tournament-winning combination, but I wanted to get some input about this question. Let's say Chewbacca is piloting the Millennium Falcon and I give him the Determination Elite Pilot Talent. Both Chewbacca's ability and the Determination description state "When you are dealt a faceup damage card, immediately…" They differ on what you do immediately, so which one comes first? If it's a faceup damage card with the Pilot trait, do I get to discard it as per the Determination upgrade? This would be a sneaky and inefficient way to keep damage off of Chewbacca, but it is a way as long as I am interpretting the rules correctly.

First question in the FAQ:

Q: If a player has multiple effects that resolve
at the same time, can he resolve them in
any order?
A: Yes.

If the damage card has the Pilot trait you would of course choose to resolve Determination first. That's roughly 1/3 of the damage deck IIRC. This looks like a good combo to me.

Oh yes the combo is really fine, i would just prefer Draw their fire or even Veteran instincts for Chewie, especially when i see that determination is kinda better on other falcon pilots and i don't like redundancies like that…

Agreed, Chewie and DTF is a better combo IMO, I was merely agreeing that the OP's combo worked as presented.