Most Hitchin representations are strongly dense

We prove that generic Hitchin representations are strongly dense: every pair of non commuting elements in their image generate a Zariski-dense subgroup of SL_n(R). The proof uses a theorem of Rapinchuk, Benyash-Krivetz and Chernousov, to show that the set of Hitchin representations is Zariski-dense in the variety of representations of a surface group in SL_n(R).