Dr. Chumley claims to see Harvey, as indeed do a number of characters in the play. It would seem that Elwood's hallucinations are contagious. Alcohol is an additional factor in Dr. Chumley's case as it's only after spending a night drinking with Elwood that he comes to see the six-foot-tall rabbit.
This is not to say that Chumley, or anyone else for that matter, actually does see Harvey in the literal sense of the word. But what he does see, in his mind's eye, is a projection of his deepest dreams and fantasies. He sees Harvey, with his alleged ability to stop time, as allowing him to leave his ordinary life behind and retreat into a fantasy world.
This is something that Chumley's been wanting to do for quite some time. For many years, he's had this elaborate fantasy of going camping with a beautiful woman just outside of Akron, Ohio. There, they will drink beer and the woman will stroke Dr. Chumley's head while he tells her his innermost secrets.
Though Harvey may not be real, he is nonetheless a sufficiently vivid hallucination to make a significant impact, not just on the life of Elwood P. Dowd, but on the lives of those he meets, including Dr. Chumley.