A two-dimensional CFT dual to a theory of semiclassical three-dimensional gravity must have a large central charge and a sparse low energy spectrum. This constrains the CFT data via the conformal bootstrap. I will define an ensemble of CFT data by averaging over OPE coefficients subject to these bootstrap constraints, and show that calculations in this ensemble reproduce aspects of semiclassical 3D gravity. I will analyze a variety of gravitational solutions, both in pure Einstein gravity and gravity coupled to massive point particles, including Euclidean wormholes with multiple boundaries and higher topology spacetimes with a single boundary. In all cases we find that the on-shell action of gravity agrees with the ensemble-averaged CFT at large c. I will also show that the bulk effective theory has random couplings induced by wormholes, providing a controlled, semiclassical realization of the Coleman-Giddings-Strominger mechanism.