  Recently, it has been found that JT gravity, which is a two-dimensional
theory with bulk action $ -\frac{1}{2}\int {\mathrm d}^2x \sqrt g\phi(R+2)$, is
dual to a matrix model, that is, a random ensemble of quantum systems rather
than a specific quantum mechanical system. In this article, we argue that a
deformation of JT gravity with bulk action $ -\frac{1}{2}\int {\mathrm d}^2x
\sqrt g(\phi R+W(\phi))$ is likewise dual to a matrix model. With a specific
procedure for defining the path integral of the theory, we determine the
density of eigenvalues of the dual matrix model. There is a simple answer if
$W(0)=0$, and otherwise a rather complicated answer.
