Although the Chief is a schizophrenic, he is the narrator of the story, so this presents an interesting challenge to the reader -- how reliable is he as a narrator?
The Chief was diagnosed as a "chronic" schizophrenic (split personality) supposedly as as a result of what he suffered during World War II. Chronic means that his illness is severe and ongoing, with little hope of improvement. He has been treated with shock treatment, which was considered a viable but barbaric last resort treatment for mental illness back in the day. In severe cases of depression, shock treatment is still used, only it is quite different than what was done to the Chief. Although the Chief has been diagnosed as a schizophrenic and has some paranoid delusions (The Combine), he is pretty clever. He pretends to be deaf and dumb. In this way, he can eavesdrop on conversations and find things out without people realizing it.