Chewbacca might be one of our favorite fictional characters of all-time, so we're sorry to say that he doesn't play a big role in The Empire Strikes Back. He spends the bulk of the film trying (and failing) to fix the Falcon's hyperspace drive and, when not, remaining firmly planted in his role as Han's sidekick.
We do see a few moments that emphasize this bond between man and Wookiee. Think back to Chewie's anguished wails after Luke and Han get trapped on the harsh Hoth wasteland. Think about when he hopelessly attacks a group of stormtroopers in a desperate attempt to save Han from being frozen. No matter the situation you find yourself in, Chewbacca is the kind of bro you want at your back.
Of course, everything is turned upside-down by the end of the film: Han has been captured by Jabba the Hutt and now Chewie and Lando must save him. Chewie might not be able to spit soliloquies like Shakespeare, but Jabba should be put on notice—this is one Wookiee you don't want to mess with.