  Let X be a smooth complex projective variety with basepoint x. We prove that
every rigid integral irreducible representation $\pi_1(X,x)\to SL (3,{\mathbb
C})$ is of geometric origin, i.e., it comes from some family of smooth
projective varieties. This partially generalizes an earlier result by K.
Corlette and the second author in the rank 2 case and answers one of their
questions.
