Tracking a randomly varying optical phase is a key task in metrology, with applications in optical communication. The best precision for optical-phase tracking has until now been limited by the quantum vacuum fluctuations of coherent light. Here, we surpass this coherent-state limit by using a continuous-wave beam in a phase-squeezed quantum state. Unlike in previous squeezing-enhanced metrology, restricted to phases with very small variation, the best tracking precision (for a fixed light intensity) is achieved for a finite degree of squeezing because of Heisenberg's uncertainty principle. By optimizing the squeezing, we track the phase with a mean square error 15 +/- 4% below the coherent-state limit.