We propose a theory to explain why, and under what circumstances, a politician gives up rent and delegates policy tasks to an independent agency. We apply this theory to monetary policy by extending a standard dynamic "New-Keynesian" stochastic general equilibrium model. This model gives a new theory of central bank independence that is unrelated to the standard inflation bias problem. We derive several new predictions and show that they are consistent with the data. Finally, we show that while instrument independence of the central bank is desirable, goal independence is not.