We obtained high angular resolution (~2") images of the 13CO(J=1-0) line and 2.7 millimeter continuum emission, and slightly lower resolution images of 12CO(J=1-0) and C18O(J=1-0) line emission toward the Herbig Ae star AB Aurigae. We resolve a circumstellar disk of diameter 780 AU (FWHM) with a velocity pattern consistent with a purely rotational disk at inclination 21.5 degrees and position angle 58.6 degrees. Using Keplerian disk models, we find a central source dynamical mass of 2.8+-0.1 Msun and a cutoff radius of 615 AU for the 13CO emission. Inclination, mass, and radius determined from 12CO and C18O observations agree with those values, given optical depth and abundance effects. As a result of the high angular resolution of our observations, we confirm the existence of spiral structure suggested by near-IR scattered light images and show that the spiral arms represent density contrasts in the disk.