High resolution observations of the extended atmospheres of asymptotic giant branch (AGB) stars can now directly confront the theories that describe stellar mass loss. Using Atacama Large Millimeter/submillimeter Array (ALMA) high angular resolution ($30\times42$~mas) observations we have, for the first time, resolved stellar rotation of an AGB star, R~Dor. We measure an angular rotation velocity of $\omega_R\sin{i}=(3.5\pm0.3)\times10^{-9}$~rad~s$^{-1}$ which indicates a rotational velocity of $|\upsilon_{\rm rot}\sin{i}|=1.0\pm0.1$~km~s$^{-1}$ at the stellar surface ($R_*=31.2$~mas at $214$~GHz). The rotation axis projected on the plane of the sky has a position angle $\Phi=7\pm6^\circ$. We find that the rotation of R Dor is two orders of magnitude faster than expected for a solitary AGB star that will have lost most of its angular momentum. Its rotational velocity is consistent with angular momentum transfer from a close companion. As a companion has not been directly detected we thus suggest R~Dor has a low-mass, close-in, companion. The rotational velocity approaches the critical velocity, set by the local sound speed in the extended envelope, and is thus expected to affect the mass loss characteristics of R~Dor.