  The mapping class group $\mathrm{Mod}_{g, 1}$ of a surface with one marked
point can be identified with an index two subgroup of $\mathrm{Aut}(\pi_1
\Sigma_g)$. For a surface of genus $g \geq 2$, we show that any action of
$\mathrm{Mod}_{g, 1}$ on the circle is either semi-conjugate to its natural
action on the Gromov boundary of $\pi_1 \Sigma_g$, or factors through a finite
cyclic group. For $g \geq 3$, all finite actions are trivial. This answers a
question of Farb.
