He could make a Chewbacca skin rug.

Yeah I would stuff him.He would make a good hat and coat holder and at the same time a cat scratch pole.

A full length fur coat for travelling to colder parts of the universe?

For one, Wookies have much longer life-spans than humans, so this is assuming he didn't die of unnatural causes. Secondly, how many folks have their dogs, stuffed when they die? Or their best friends for that matter? My feeling is he'd bring him back to his home planet of Kashyyyk for a proper burial with his kind.

Chewbacca gumbo

I see you're a real Star Wars fan, so I'll give you the canonical answer. He is already dead, and quite vaporised, so there isn't much can be done with him, execpt keep him as a small jar of plasma. You can find it all on Wokieepedia.com, but here's a short version: In 25 ABY (After the Battle of Yavin), Chewbacca, Han Solo and his youngest son Anakin were sent to pick up a shipment on Sernpidal. When they arrived, they discovered that Dobido (a moon), was headed on a collision course with Sernpidal. Anakin calculated the moon would collide with Sernpidal in seven hours. As the winds picked up, Anakin was knocked into the distance, causing Chewie to run after him. Chewie was able to bring Anakin to safety on the Falcon, but another blast of wind knocked him out of reach. Anakin piloted the Falcon, while his father stood on the entrance ramp hoping to lift Chewie up, but was forced to flee when he realized it was too late to save Chewie. The Wookiee stood in the moon's trajectory, howling defiantly, and was crushed to death with those Sernpidalians who could not escape. Wookiees would take pride in the fact that Chewbacca died honoring his life debt, as well as the fact that it literally took an entire moon to kill him. To commemorate his heroic efforts, the villagers of Kashyyyk built a tree memorial in his honor. Han visited the tree memorial of Chewbacca and stabbed Anakin Solo's lightsaber deep into the tree, so that anyone who would need it in the future could use it.''