We say the same thing about Newfoundland English. "I don't have an accent? Give me a drink or two, and you'll hear it!"
A friend finally said, "You know, every Newfoundlander I've ever met has said that. Maybe there is no Newfoundland accent. Maybe being drunk is the Newfoundland accent."
And so I present to you:
Maybe Chiac is simply drunken Quebec French?