We show that oil production from existing wells in Texas does not respond to price incentives. Drilling activity and costs, however, do respond strongly to prices. To explain these facts, we reformulate Hotelling's (1931) classic model of exhaustible resource extraction as a drilling problem: firms choose when to drill, but production from existing wells is constrained by reservoir pressure, which decays as oil is extracted. The model implies a modified Hotelling rule for drilling revenues net of costs and explains why production is typically constrained. It also rationalizes regional production peaks and observed patterns of price expectations following demand shocks.