grin like a Cheshire cat have a broad fixed smile on your face.

☞ The Cheshire cat with its broad grin is best known for its appearance (and disappearance) in Lewis Carroll's Alice's Adventures in Wonderland (1865), but the expression is recorded from the first half of the 19th century. Its origins remain enigmatic, although it has been claimed that Cheshire cheeses were at one time marked with the face of a smiling cat. (There is no such breed as an actual 'Cheshire cat'.)