One of the great injustices of Star Wars: Episode IV - A New Hope has been thankfully undone with the power of the comic book retcon. Chewbacca has now gotten his medal for service to the Rebel Alliance - which he then gave away.
In the pages of Chewbacca #5, the final issue of a Marvel Comics mini-series starring the growling Wookiee by Gerry Duggan and Phil Noto, it was revealed that he got a medal at the ceremony after the destruction of the first Death Star after all. It wasn't shown on screen, perhaps because they didn't have a ribbon long enough to secure it over his head? In the comic, he gives it to his new young friend, Zarro, who he just had quite the adventure with.
She does question why he wouldn't want it for himself, and the only answer we get is "Yeah, it would kind of clash with your whole warrior vibe."
So you see, Chewbacca got his medal - he was just too big and badass to bother wearing it.
For fans not familiar with comic books, whenever something like this is is done in their pages, it's called a "retcon" or retroactive continuity. Here, something is added to the past, and from that point forward, it's meant to be considered part of the ongoing story, as if it was there all along.
So Chewie got his medal. Everyone can stop calling the Rebel Alliance racist now.