Forward-looking agents care about expected future utility flows, and hence have higher current felicity if they are optimistic. This paper studies utility-based biases in beliefs by supposing that beliefs maximize average felicity, optimally balancing this benefit of optimism against the costs of worse decision making. A small optimistic bias in beliefs typically leads to first-order gains in anticipatory utility and only second-order costs in realized outcomes. In a portfolio choice example, investors overestimate their return and exhibit a preference for skewness; in general equilibrium, investors' prior beliefs are endogenously heterogeneous. In a consumption-saving example, consumers are both overconfident and overoptimistic.