This paper considers a pure exchange stochastic overlapping generations model in which, on each date, an economy faces an aggregate endowment shock. On each date, a young agent and an old agent simultaneously decide how much of their respective endowments to transfer to the other agent; however, a young agent cannot make promises about how much he or she will give when old. In this sense, an economy faces a limited commitment constraint. This paper characterizes an efficient intergenerational risk sharing allocation that satisfies a limited commitment constraint, and also studies the role of money and history in a stochastic overlapping generations economy.