This paper presents an infinite-horizon version of intergenerational utilitarianism. By studying discounted utilitarianism as the discount factor tends to one, we obtain a new welfare criterion: limit-discounted utilitarianism (LDU). We show that LDU meets standard assumptions of efficiency, equity, and interpersonal comparability, but allows us to compare more pairs of utility streams than commonly-used utilitarian criteria, including the overtaking criterion and the catching-up criterion. We also introduce a principle of compensation for postponements of utility streams and use it to characterize the LDU criterion on a restricted domain.