Cheney face Share definition Flag A novacane-induced downward drooping lip resulting from a visit to the dental office. I went to the dentist with Andrea yesterday, and by the time they were done with her she had really bad case of Cheney face. Cheney face by ashburyclowden April 6, 2013 0 0 Get merch Get the Cheney face mug. Buy Now — $32.95 See more merch