A $q$-anaolg of the sixth Painlev\'e equation

A $q$-difference analog of the sixth Painlev'e equation is presented. It arises as the condition for preserving the connection matrix of linear $q$-difference equations, in close analogy with the monodromy preserving deformation of linear differential equations. The continuous limit and special solutions in terms of $q$-hypergeometric functions are also discussed.