The hot gaseous halos of galaxies likely contain a large amount of mass and are an integral part of galaxy formation and evolution. The Milky Way has a 2e6 K halo that is detected in emission and by absorption in the OVII resonance line against bright background AGNs, and for which the best current model is an extended spherical distribution. Using XMM-Newton RGS data, we measure the Doppler shifts of the OVII absorption-line centroids toward an ensemble of AGNs. These Doppler shifts constrain the dynamics of the hot halo, ruling out a stationary halo at about 3sigma and a corotating halo at 2sigma, and leading to a best-fit rotational velocity of 183+/-41 km/s for an extended halo model. These results suggest that the hot gas rotates and that it contains an amount of angular momentum comparable to that in the stellar disk. We examined the possibility of a model with a kinematically distinct disk and spherical halo. To be consistent with the emission-line X-ray data the disk must contribute less than 10% of the column density, implying that the Doppler shifts probe motion in the extended hot halo.