In this paper, we elaborate on an idea initially developed by Weitzman (1998) that justifies taking the lowest possible discount rate for far-distant future cash flows. His argument relies on the arbitrary assumption that when the future rate of return of capital (RRC) is uncertain, one should invest in any project with a positive expected net present value. We examine an economy with a risk-averse representative agent facing an uncertain evolution of the RRC. In this context, we characterize the socially efficient stochastic consumption path, which allows us in turn to use the Ramsey rule to characterize the term structure of socially efficient discount rates. We show that Weitzman’s claim is qualitatively correct if shocks on the RRC are persistent. On the contrary, in the absence of any serial correlation in the RRC, the term structure of discount rates should be flat.