Real-time specular x-ray reflectivity of pulsed laser deposited BiFeO3 films exhibits unit-cell oscillations, with diffuse scattering intensity out-of-phase with the specular intensity. The growth mode is thus identified as nucleation and coalescence of unit-cell height islands. The growth rate is insensitive to the deposition rate, suggesting self-limiting growth. Beyond several monolayers the diffuse intensity increases abruptly, signaling a transition from two-dimensional to three-dimensional growth. Ex situ atomic force microscopy shows that mounds merge after a few more deposited layers, leaving arrays of mesas with some holes due to incomplete coalescence.