We present sub-arcsecond images of AB Auriga obtained with the IRAM Plateau de Bure interferometer in the isotopologues of CO, and in continuum at 3 and 1.3 mm. Instead of being centrally peaked, the continuum emission is dominated by a bright, asymmetric (spiral-like) feature at about 140 AU from the central star. The large scale molecular structure suggests the AB Aur disk is inclined between 23 and 43 degrees, but the strong asymmetry of the continuum and molecular emission prevents an accurate determination of the inclination of the inner parts. We find significant non-Keplerian motion, with a best fit exponent for the rotation velocity law of 0.41 +/- 0.01, but no evidence for radial motions. The disk has an inner hole about 70 AU in radius. The disk is warm and shows no evidence of depletion of CO. The dust properties suggest the dust is less evolved than in typical T Tauri disks. Both the spiral-like feature and the departure from purely Keplerian motions indicates the AB Aur disk is not in quasi-equilibrium. Disk self-gravity is insufficient to create the perturbation. This behavior may be related either to an early phase of star formation in which the Keplerian regime is not yet fully established and/or to a disturbance of yet unknown origin. An alternate, but unproven, possibility is that of a low mass companion located about 40 AU from AB Aur.