It was proven recently that JT gravity can be defined as an ensemble of L× L Hermitian matrices. We point out that the eigenvalues of the matrix correspond in JT gravity to FZZT-type boundaries on which spacetimes can end. We then investigate an ensemble of matrices with 1≪ N≪ L eigenvalues held fixed. This corresponds to a version of JT gravity which includes N FZZT type boundaries in the path integral contour and which is found to emulate a discrete quantum chaotic system. In particular this version of JT gravity can capture the behavior of finite-volume holographic correlators at late times, including erratic oscillations.