Outside of there allegedly being some people asking to purchase the Falcon from Han (and Solo refusing any sale), there’s little information on the circumstances surrounding the Falcon‘s ownership. The only thing that seems to be certain at this juncture is that Han does lose the ship somehow prior to the events of Episode VII, which explains Han’s now famous line from the second Force Awakens trailer (“Chewie… we’re home.”)
Making Star Wars‘ report indicates that, as far as the new Star Wars canon is concerned, Han and Chewbacca’s history is as follows:
Chewbacca is captured and put into slavery in the aftermath of Revenge of the Sith and the invasion of Kashyyyk. Han Solo frees the Wookiee and therefore Chewbacca owes Han Solo a life debt.
source Making of Star Wars