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.