  The SL(3,C)-representation variety R of a free group F arises naturally by
considering surface group representations for a surface with boundary. There is
a SL(3,C)-action on the coordinate ring of R by conjugation. The geometric
points of the subring of invariants of this action is an affine variety X. The
points of X parametrize isomorphism classes of completely reducible
representations. We show the coordinate ring C[X] is a complex Poisson algebra
with respect to a presentation of F imposed by the surface. Lastly, we work out
the bracket on all generators when the surface is a three-holed sphere or a
one-holed torus.
