  Iorgov, Lisovyy, and Teschner established a connection between isomonodromic
deformation of linear differential equations and Liouville conformal field
theory at $c=1$. In this paper we present a $q$ analog of their construction.
We show that the general solution of the $q$-Painlev\'e VI equation is a ratio
of four tau functions, each of which is given by a combinatorial series arising
in the AGT correspondence. We also propose conjectural bilinear equations for
the tau functions.
