  We propose a precise reformulation of 3d quantum gravity with negative
cosmological constant in terms of a topological quantum field theory based on
the quantization of the Teichm\"uller space of Riemann surfaces that we refer
to as ``Virasoro TQFT.'' This TQFT is similar, but importantly not equivalent,
to $\text{SL}(2,\mathbb{R})$ Chern-Simons theory. This sharpens the folklore
that 3d gravity is related to $\text{SL}(2,\mathbb{R})$ Chern-Simons theory
into a precise correspondence, and resolves some well-known issues with this
lore at the quantum level. Our proposal is computationally very useful and
provides a powerful tool for the further study of 3d gravity. In particular, we
explain how together with standard TQFT surgery techniques this leads to a
fully algorithmic procedure for the computation of the gravity partition
function on a fixed topology exactly in the central charge. Mathematically, the
relation leads to many nontrivial conjectures for hyperbolic 3-manifolds,
Virasoro conformal blocks and crossing kernels.
