The neural mechanisms underlying hunger are poorly understood. AgRP neurons are activated by energy deficit and promote voracious food consumption, suggesting these cells may supply the fundamental hunger drive that motivates feeding. However recent in vivo recording experiments revealed that AgRP neurons are inhibited within seconds by the sensory detection of food, raising the question of how these cells can promote feeding at all. Here we resolve this paradox by showing that brief optogenetic stimulation of AgRP neurons before food availability promotes intense appetitive and consummatory behaviors that persist for tens of minutes in the absence of continued AgRP neuron activation. We show that these sustained behavioral responses are mediated by a long-lasting potentiation of the rewarding properties of food and that AgRP neuron activity is positively reinforcing. These findings reveal that hunger neurons drive feeding by transmitting a positive valence signal that triggers a stable transition between behavioral states.