We have measured the stellar kinematic profiles of NGC 3379 along four position angles, using absorption lines in spectra obtained with the Multiple Mirror Telescope. We derive a far more detailed description of the kinematic fields through the main body of the galaxy than could be obtained from previous work. Our data extend 90" from the center, at essentially seeing-limited resolution out to 17". The derived mean velocities and dispersions have total errors (internal and systematic) better than +/-10 km s(-1), and frequently better than 5 km s(-1), out to 55". We find very weak (3 km s(-1)) rotation on the minor axis interior to 12" and no detectable rotation above 6 km s(-1) from 12" to 50" or above 16 km s(-1) out to 90" (95% confidence limits). However, a Fourier reconstruction of the mean velocity field from all four sampled PAs does indicate a approximate to 5 degrees twist of the kinematic major axis, in the direction opposite to the known isophotal twist. The h(3) and h(4) parameters are found to be generally small over the entire observed region. The azimuthally averaged dispersion profile joins smoothly at large radii with the velocity dispersions of planetary nebulae. Unexpectedly, we find sharp bends in the major axis rotation curve, also visible (though less pronounced) on the diagonal position angles. The outermost bend closely coincides in position with other sharp kinematic features: an abrupt flattening of the dispersion profile, and local peaks in h(3) and h(4). All of these features are in a photometrically interesting region in which the surface brightness profile departs significantly from an r(1/4) law. Features such as these are not generally known in elliptical galaxies owing to a lack of data at comparable resolution. Very similar behavior, however, is seen the kinematics of the edge-on SO galaxy NGC 3115. We discuss the suggestion that NGC 3379 could be a misclassified SO galaxy; preliminary results from dynamical modeling indicate that it may be a flattened, weakly triaxial system seen in an orientation that makes it appear round.