  Let $\Gamma$ be the mapping class group of an oriented surface $\Sigma$ of
genus g with r boundary components. We prove that the first cohomology group
$H^1(\Gamma, O(M_{SL(2, C)})^*)$ is non-trivial, where the coefficient module
is the dual of the space of algebraic functions on the $SL(2, C)$ moduli space
over $\Sigma$.
