  We study the motive of the moduli space of semistable Higgs bundles of
coprime rank and degree on a smooth projective curve C over a field k under the
assumption that C has a rational point. We show this motive is contained in the
thick tensor subcategory of Voevodsky's triangulated category of motives with
rational coefficients generated by the motive of C. Moreover, over a field of
characteristic zero, we prove a motivic non-abelian Hodge correspondence: the
integral motives of the Higgs and de Rham moduli spaces are isomorphic.
