The ability to follow the gaze of another human plays a critical role in cognitive development. Recent experimental results indicate that gaze following is not merely an imitation of head movement. We propose that children learn a probabilistic model of the consequences of their movements, and later use this learned model of self as a surrogate for another human. We introduce a Bayesian model where gaze following occurs as a consequence of goal inference in a learned probabilistic graphical model. Bayesian inference over this learned model provides both an estimate of anothers fixation location and the appropriate action to follow their gaze. The model can be regarded as a probabilistic instantiation of Meltzoffs Like me hypothesis. We present simulation results based on a nonparametric Gaussian process implementation of the model, and compare the models performance to infant gaze following results.