We present the first example of a phase transition in a nonequilibrium steady state that can be argued analytically to be first order. The system of interest is a two-species reaction-diffusion problem whose control parameter is the total density p. Mean-field theory predicts a second-order transition between two
stationary states at a critical density \=\c. We develop a phenomenological picture that instead predicts a first-order transition below the upper critical dimension dc=4. This picture is confirmed by hysteresis found in numerical simulations, and by the study of a renormalization-group improved equation of state. The latter approach is inspired by the ColemanWeinberg mechanism in QED.