  We prove that the only closed, embedded ancient solutions to the curve
shortening flow on $\mathbb{S}^2$ are equators or shrinking circles, starting
at an equator at time $t=-\infty$ and collapsing to the north pole at time
$t=0$. To obtain the result, we first prove a Harnack inequality for the curve
shortening flow on the sphere. Then an application of the Gauss-Bonnet, easily
allows us to obtain curvature bounds for ancient solutions leading to backwards
smooth convergence to an equator. To complete the proof, we use an Aleksandrov
reflection argument to show that maximal symmetry is preserved under the flow.
