Extinction promotes abstinence from drug seeking. Extinction expression is an active process, dependent on infralimbic prefrontal cortex (ilPFC). However, the neurocircuitry mediating extinction expression is unknown. Here we studied the neural mechanisms for expression of extinction of alcoholic beer seeking in rats. We first examined the pattern of activation in prefrontal cortex projections to medial dorsal hypothalamus (MDH) (i.e., perifornical and dorsomedial nuclei) during extinction expression. Double labeling for retrograde tracer cholera toxin B subunit (CTb) and the neuronal activity marker c-Fos revealed significant recruitment of MDH projecting ilPFC neurons during extinction expression. We then studied the causal role of MDH in inhibiting alcoholic beer seeking during extinction expression. MDH infusion of the inhibitory neuropeptide cocaine- and amphetamine-regulated transcript prevented extinction expression, showing that MDH is necessary for extinction expression. Next we examined the pattern of activation in MDH projections to paraventricular thalamus (PVT) during extinction expression. Double labeling for CTb and c-Fos revealed significant recruitment of PVT projecting MDH neurons during extinction expression. We also showed, using triple-label immunofluorescence, that the majority of PVT projecting extinction neurons express prodynorphin, suggesting that actions at κ opioid receptors (KORs) in PVT may be critical for inhibiting alcoholic beer seeking. Consistent with this, infusions of a KOR agonist into PVT prevented reinstatement of alcoholic beer seeking showing that PVT KOR activation is sufficient to inhibit alcoholic beer seeking. Together, these findings identify a role for MDH and its ilPFC afferents and PVT efferents in inhibiting alcoholic beer seeking during extinction expression.