When people stop believing in God, they don't believe in nothing — they believe in anything.
Source, in full
This quotation actually comes from page 211 of Émile Cammaerts' book The Laughing Prophet: The Seven Virtues and G. K. Chesterton (1937) in which he quotes Chesterton as having Father Brown say, in "The Oracle of the Dog" (1923): "It's the first effect of not believing in God that you lose your common sense." Cammaerts then interposes his own analysis between further quotes from Father Brown: "'It's drowning all your old rationalism and scepticism, it's coming in like a sea; and the name of it is superstition.' The first effect of not believing in God is to believe in anything: 'And a dog is an omen and a cat is a mystery.'" Note that the remark about believing in anything is outside the quotation marks — it is Cammaerts. The correct attribution was reportedly first traced by Pasquale Accardo. It was also credited to Nigel Rees (as cited in First Things, 1997).