This paper proposes a novel theory of reserve accumulation that emphasizes the role of an independent central bank in an environment where the government lacks fiscal discipline. I use panel data for 11 Latin American countries to document the tendency of more independent central banks to accumulate more international reserves. Motivated by this novel fact, I develop a quantitative sovereign default model with an independent central bank that can accumulate international reserves. I show that, if the government is more impatient than the central bank and households, in equilibrium, the government issues more debt than what is socially optimal and the central bank accumulates reserves to offset government borrowing. A key insight is that the government can issue more debt for any level of reserves but chooses not to because it would increase sovereign spreads, making it more costly to borrow. Quantitatively, I show that the central bank independence channel accounts for 83% of the average level of reserves observed in Mexico from 1994 to 2017. I find that accumulating reserves by 7.2% of the GDP reduces the net debt position by 3.3% of GDP and increases social welfare by 0.1%.