We can track Han and Luke's advancement through the ranks in the original trilogy pretty easily. What about Chewie? Did he have a formal rank? If so, what was his rank in each of the movies in the original trilogy? Or was he just an aide to Han?
Currently, there is no mention in any G/Disney Canon or EU/Legends material where Chewbacca has ever received an official rank in the Rebel Alliance or the New Republic.
This has never been explained, but one of the more common fan-explanations I've seen is that since Chewbacca has sworn a debt to Han, accepting an official position in the Alliance could possibly require him to unwillingly serve away from Han.