We present particle-in-cell simulations of collisionless magnetic reconnection in a system (like the magnetopause) with a large density asymmetry across the current layer. In the presence of an ambient component of the magnetic field perpendicular to the reconnection plane the gradient creates a diamagnetic drift that advects the X-line with the electron diamagnetic velocity. When the relative drift between the ions and electrons is of the order the Alfv¿n speed the large scale outflows from the X-line necessary for fast reconnection cannot develop and the reconnection is suppressed. We discuss how these effects vary with both the plasma ¿ and the shear angle of the reconnecting field and discuss observational evidence for diamagnetic stabilization at the magnetopause.