Atomistic modeling of chemically reactive systems has so far relied on either expensive ab initio methods or bond-order force fields requiring arduous parametrization. Here, we describe a Bayesian active learning framework for autonomous ``on-the-fly'' training of fast and accurate reactive many-body force fields during molecular dynamics simulations. At each time step, predictive uncertainties of a sparse Gaussian process are evaluated to automatically determine whether additional ab initio training data are needed. We introduce a general method for mapping trained kernel models onto equivalent polynomial models whose prediction cost is much lower and independent of the training set size. As a demonstration, we perform direct two-phase simulations of heterogeneous H2 turnover on the Pt(111) catalyst surface at chemical accuracy. The model trains itself in three days and performs at twice the speed of a ReaxFF model, while maintaining much higher fidelity to DFT and excellent agreement with experiment.