A Madden-Julian Oscillation (MJO) is a massive weather event consisting of deep convection coupled with atmospheric circulation, moving slowly eastward over the Indian and Pacific Oceans. Despite its enormous influence on many weather and climate systems worldwide, it has proven very difficult to simulate an MJO because of assumptions about cumulus clouds in global meteorological models. Using a model that allows direct coupling of the atmospheric circulation and clouds, we successfully simulated the slow eastward migration of an MJO event. Topography, the zonal sea surface temperature gradient, and interplay between eastward- and westward-propagating signals controlled the timing of the eastward transition of the convective center. Our results demonstrate the potential making of month-long MJO predictions when global cloud-resolving models with realistic initial conditions are used.