An exhaustive first-principles study of the energetics of B-Si interstitial complexes of various configurations and charge states is used to elucidate the diffusion mechanism of B in Si. Total energy calculations and molecular dynamics simulations show that B diffuses by an interstitialcy mechanism. Substitutional B captures a Si interstitial with a binding energy of 0.90 eV. This complex is itself a fast diffuser, with no need to first ``kick out'' the B into an interstitial channel. The migration barrier is about 0.68 eV. Kinetic Monte Carlo simulations confirm that this mechanism leads to a decrease in the diffusion length with increasing temperature, as observed experimentally.