We consider the intertemporal problem of optimally consuming a natural resource and exploring for new sources of supply of that resource. Resource consumption yields social utility while the exploration effort controls the uncertainty in the timings of discoveries as well as their magnitudes. The objective is to choose an optimal consumption and exploration policy so as to maximize the expected discounted utility of consumption net of the exploration cost over an infinite planning horizon. We present a controlled storage process model of the problem and under reasonable conditions we characterize the existence and the properties of optimal policies and prices.