  We investigate the kinematic properties of Galactic HII regions using radio
recombination line (RRL) emission detected by the Australia Telescope Compact
Array (ATCA) at 4-10 GHz and the Jansky Very Large Array (VLA) at 8-10 GHz. Our
HII region sample consists of 425 independent observations of 374 nebulae that
are relatively well isolated from other, potentially confusing sources and have
a single RRL component with a high signal-to-noise ratio. We perform Gaussian
fits to the RRL emission in position-position-velocity data cubes and discover
velocity gradients in 178 (42%) of the nebulae with magnitudes between 5 and
200 m/s/arcsec. About 15% of the sources also have a RRL width spatial
distribution that peaks toward the center of the nebula. The velocity gradient
position angles appear to be random on the sky with no favored orientation with
respect to the Galactic Plane. We craft HII region simulations that include
bipolar outflows or solid body rotational motions to explain the observed
velocity gradients. The simulations favor solid body rotation since, unlike the
bipolar outflow kinematic models, they are able to produce both the large, > 40
m/s/arcsec, velocity gradients and also the RRL width structure that we observe
in some sources. The bipolar outflow model, however, cannot be ruled out as a
possible explanation for the observed velocity gradients for many sources in
our sample. We nevertheless suggest that most HII region complexes are rotating
and may have inherited angular momentum from their parent molecular clouds.
