  We measured the angular rotation and proper motion of the Triangulum Galaxy
(M33) with the Very Long Baseline Array by observing two H2O masers on opposite
sides of the galaxy. By comparing the angular rotation rate with the
inclination and rotation speed, we obtained a distance of 730 +/- 168
kiloparsecs. This distance is consistent with the most recent Cepheid distance
measurement. M33 is moving with a velocity of 190 +/- 59 km/s relative to the
Milky Way. These measurements promise a new method to determine dynamical
models for the Local Group and the mass and dark matter halos of M31, M33 and
the Milky Way.
