  We show that for $S$ a closed surface of genus at least $3$, the set of
Hitchin representations of $\pi_1(S)$ with image in
$\operatorname{SL}(n,\mathbf{Q})$ is dense in the Hitchin component. When
$n=2$, we recover a particular case of a result of Takeuchi but using a
completely different method.
