We propose in this paper a model of optimal Carbon Capture and Storage in which the reservoir of sequestered carbon is leaky, and pollution eventually is released into the atmosphere. We formulate the social planner problem as an optimal control program and we describe the optimal consumption paths as a function of the initial conditions, the physical constants and the economical parameters. In particular, we show that the presence of leaks may lead to situations which do not occur otherwise, including that of non-monotonous price paths for the energy.