At the end of the day, he's still a kid and kids don't like chores and sometimes they just want their own way. Non ASD kids can be difficult too. :) If he is high functioning enough to do chores he is certainly capable of learning how to behave properly and cooperate in a family unit, it will just take consistency and patience on your part. A lot of it. I am very against allowing Aspergers to be a crutch for poor behavior (Specifically for myself and my son). The minute you give in and say I guess he needs to do what he wants when he wants because he has ASD is when you send the message that he can successfully manipulate you, and that he isn't held to the same standard as his "normal" siblings. It will do nobody any favors in the long run, especially not him. Nothing you don't already know, I'm sure!
I agree with Fauwks. Options, logic and feelings of control go a long way. If your son finds that not doing what he's told results in x but doing his chores results in y, he will eventually choose y because that's the better option right? Consistency is key. Also explanations. Why is this chore important? Why is HE the one chosen to do that chore? If he's old enough to understand anyway. I know that worked for me when I was growing up. If it made sense and seemed fair I didn't have a problem with being asked to do stuff I didn't want to do. I HATED being treated differently from my siblings. And that was long before I had a diagnosis of something other than "gifted."
Anyway, I'm in your same boat. Literally nothing is easy to do with my son right now. Even getting him to cooperate in going somewhere he specifically asked to go is a challenge! I've stopped telling him to do this or asking him to do this, but instead say "let's feed the dog!" Or "do you want to feed the dog or clean up your toys?" When I need to go to the grocery store I'll say "want to go drive the cart at the store or stay here and clean?" He'll always choose the store. :)
Good luck! None of us really knows anything, we're all still figuring things out.