How should monetary authorities react to an oil price shock? The New Keynesian literature has concluded that ensuring perfect price stability is optimal. Yet, the contrast between theory and practice is striking: Inflation targeting central banks typically favor a longer run approach to price stability. The first contribution of this paper is to show that because oil cost shares vary with oil prices, policies that perfectly stabilize prices entail large welfare costs, which explains the reluctance of policymakers to enforce them. The policy trade-off faced by monetary authorities is meaningful because oil (energy) is an input to both production and consumption. Welfare-based optimal policies rely on unobservables, which makes them hard to implement and communicate. The second contribution of this paper is thus to analytically derive a simple interest rate rule that mimics the optimal plan in all dimensions but that only depends on observables: core inflation and the growth rates of output and oil prices. It turns out that optimal policy is hard on core inflation but cushions the economy against the real consequences of an oil price shock by reacting strongly to output growth and negatively to oil price changes. Following a Taylor rule or perfectly stabilizing prices during an oil price shock are very costly alternatives.