Inside a standard growth model with exhaustible resources, we study the optimal growth policy of an economy submitted to a climate constraint, taking the form of a ceiling over admissible atmospheric carbon concentrations. The optimal scenario is a three phases path: a rise of carbon concentrations until the carbon cap is attained followed by a time phase constrained by the ceiling on possible emissions and a last unconstrained phase of resource depletion. Depending upon the primitives of the model we show that the optimal path may be of two main kinds: paths characterized by a positive growth of the economy and paths corresponding to a complex structural adjustment process involving negative growth during some time interval.