A challenge in treating substance use disorder is that successful treatment often does not persist, resulting in relapse and continued drug seeking. One approach to persistently weaken drug-seeking behaviors is to pair exposure to drug-associated cues or behaviors with delivery of a compound that may strengthen the inhibition of the association between drug cues and behavior. We evaluated whether a selective histone deacetylase 3 (HDAC3) inhibitor could promote extinction and weaken contextual control of operant drug seeking after intravenous cocaine self-administration. Male Long-Evans rats received a systemic injection of the HDAC3 inhibitor RGFP966 either before or immediately after the first extinction session. Persistence of extinction was tested over subsequent extinction sessions, as well as tests of reinstatement that included cue-induced reinstatement, contextual renewal, and cocaine-primed reinstatement. Additional extinction sessions occurred between each reinstatement test. We also evaluated effects of RGFP966 on performance and motivation during stable fixed ratio operant responding for cocaine and during a progressive ratio of reinforcement. RGFP966 administered before the first extinction session led to significantly less responding during subsequent extinction and reinstatement tests compared to vehicle-injected rats. Follow-up studies found that these effects were not likely due to a performance deficit or a change in motivation to self-administer cocaine, as injections of RGFP966 had no effect on stable responding during a fixed or progressive ratio schedule. In addition, RGFP966 administered just after the first extinction session had no effect during early extinction and reinstatement tests, but weakened long-term responding during later extinction sessions. These results suggest that a systemic injection of a selective HDAC3 inhibitor can enhance extinction and suppress reinstatement after cocaine self-administration. The finding that behavioral and pharmacological manipulations can be combined to decrease drug seeking provides further potential for treatment by epigenetic modulation.