  We prove that curve shortening flow on the round sphere displays sharp
chord-arc improvement, precisely as in the planar setting (Andrews and Bryan,
Comm. Anal. Geom., 2011). As in the planar case, the sharp estimate implies
control on the curvature, resulting in a direct and efficient proof that simple
spherical curves either contract to round points (in finite time) or converge
to great circles (in infinite time).
