Hamilton proved that positive sectional curvature, sec > 0, is preserved under Ricci flow in dimensions 2 and 3. However, as shown by Bettiol and Krishnan, this is no longer true beginning in dimension 4. In fact, Cheung and Wallach and, later, González-Álvaro and Zarei showed that sec > 0 is not preserved under the added assumption that the starting metric is homogenous. We will show that, in contrast to these results, Ricci flow does in fact preserve the set of homogeneous sec > 0 metrics on a sphere of any dimension. This is joint work with David González-Álvaro and Masoumeh Zarei.