Brillouin laser oscillators offer powerful and flexible dynamics as the basis for mode-locked lasers, microwave oscillators, and optical gyroscopes in a variety of optical systems. However, Brillouin interactions are exceedingly weak in conventional silicon photonic waveguides, stifling progress towards silicon-based Brillouin lasers. The recent advent of hybrid photonic-phononic waveguides has revealed Brillouin interactions to be one of the strongest and most tailorable nonlinearities in silicon. Here, we harness these engineered nonlinearities to demonstrate Brillouin lasing in silicon. Moreover, we show that this silicon-based Brillouin laser enters an intriguing regime of dynamics, in which optical self-oscillation produces phonon linewidth narrowing. Our results provide a platform to develop a range of applications for monolithic integration within silicon photonic circuits.