The constrained density functional theory-configuration interaction (CDFT-CI) method has previously been used to calculate ground-state energies and barrier heights, and to describe electronic excited states, in particular conical intersections. However, the method has been limited to evaluating the electronic energy at just a single nuclear configuration, with the gradient of the energy being available only via finite difference. In this paper, we present analytic gradients of the CDFT-CI energy with respect to nuclear coordinates, which gives the potential for accurate geometry optimization and molecular dynamics on both the ground and excited electronic states, a realm which is currently quite challenging for electronic structure theory. We report the performance of CDFT-CI geometry optimization for representative reaction transition states as well as molecules in an excited state. The overall accuracy of CDFT-CI for computing barrier heights is essentially unchanged whether the energies are evaluated at geometries obtained from quadratic configuration-interaction singles and doubles (QCISD) or CDFT-CI, indicating that CDFT-CI produces very good reaction transition states. These results open up tantalizing possibilities for future work on excited states.National Science Foundation (U.S.) (CAREER Award CHE-0547877)David & Lucile Packard Foundation (Fellowship)