Representations of surface groups into SL(3,C) are parameterized by conjugacy classes. When classes whose closures intersect are identified, the space of representations forms an algebraic quotient known as a character variety. This moduli space has a natural Poisson geometry which depends on the surface. For surfaces with Euler characteristic -1 the moduli space is an affine degree 6 hyper-surface in C^9. We use the explicit structure of the defining ideal of polynomial relations to work out the Poisson bivector explicitly for both the three-holed sphere and the one-holed torus.