  Denote the free group on two letters by F2 and the SL(3,C)-representation
variety of F2 by R = Hom(F2, SL(3,C)). There is a SL(3,C)-action on the
coordinate ring of R, and the geometric points of the subring of invariants is
an affine variety X. We determine explicit minimal generators and defining
relations for the subring of invariants and show X is a degree 6 hyper-surface
in C9 mapping onto C8. Our choice of generators exhibit Out(F2) symmetries
which allow for a succinct expression of the defining relations.
