The ``western arc'' and ``minicavity''(approximately 3^'' southwest of Sgr A*) of the Galactic center H II region Sgr A West have been imaged in the H 92 alpha line at 8.3 GHz with the VLA. The kinematics of the ionized gas in the inner 1.5 parsecs of the Galactic center have been determined. The western arc, with an inner radius of 1 pc, appears to be in circular rotation about a point near Sgr A*, with an enclosed mass of ~ 3.5 * 10^6 M_o. Toward the minicavity, a large velocity gradient (> 600 km s^-1 pc^-1) is observed along the eastern rim and uniformly large velocities are observed along the western rim. The velocity field of the minicavity is interpreted as gas in a hyperbolic orbit about Sgr A*. Based on this model, the gas is orbiting a point at the position of Sgr A* with a mass of ~3.0 * 10^6 M_o.