Finitely generated profinitely dense free groups in higher rank semi-simple groups

We prove that if Gamma is an arithmetic subgroup of a non-compact linear semi-simple group G such that the associated simply connected algebraic group over Q has the so-called congruence subgroup property, then Gamma contains a finitely generated profinitely dense free subgroup. As a corollary we obtain a f.g.p.d.f subgroup of SLn(Z) (n greater than or equal to 3). More generally, we prove that if Gamma is an irreducible arithmetic non-cocompact lattice in a higher rank group, then Gamma contains f.g.p.d.f groups.