  In recent work we computed the path integral of three-dimensional gravity
with negative cosmological constant on spaces which are topologically a torus
times an interval. Here we employ a modular bootstrap to show that the
amplitude is completely fixed by consistency conditions and a few basic inputs
from gravity. This bootstrap is notably for an ensemble of CFTs, rather than
for a single instance. We also compare the 3d gravity result with the Narain
ensemble. The former is well-approximated at low temperature by a random matrix
theory ansatz, and we conjecture that this behavior is generic for an ensemble
of CFTs at large central charge with a chaotic spectrum of heavy operators.
