Quantum cascade lasers are a unique laboratory for studying nonlinear laser dynamics because of their high intracavity intensity, strong intersubband optical nonlinearity, and an unusual combination of relaxation time scales. Here we investigate the nonlinear coupling between the transverse modes of quantum cascade lasers. We present evidence for stable phase coherence of multiple transverse modes over a large range of injection currents. We explain the phase coherence by a four-wave mixing interaction originating from the strong optical nonlinearity of the gain transition. The phase-locking conditions predicted by theory are supported by spectral data and both near- and far-field mode measurements.