Oscillations in the hippocampal network during sleep are proposed to play a role in memory storage by patterning neuronal ensemble activity. Here we show that following single-trial fear learning, sleep deprivation (which impairs memory consolidation) disrupts coherent firing rhythms in hippocampal area CA1. State-targeted optogenetic inhibition of CA1 parvalbumin-expressing (PV+) interneurons during postlearning NREM sleep, but not REM sleep or wake, disrupts contextual fear memory (CFM) consolidation in a manner similar to sleep deprivation. NREM-targeted inhibition disrupts CA1 network oscillations which predict successful memory storage. Rhythmic optogenetic activation of PV+ interneurons following learning generates CA1 oscillations with coherent principal neuron firing. This patterning of CA1 activity rescues CFM consolidation in sleep-deprived mice. Critically, behavioral and optogenetic manipulations that disrupt CFM also disrupt learning-induced stabilization of CA1 ensembles' communication patterns in the hours following learning. Conversely, manipulations that promote CFM also promote long-term stability of CA1 communication patterns. We conclude that sleep promotes memory consolidation by generating coherent rhythms of CA1 network activity, which provide consistent communication patterns within neuronal ensembles. Most importantly, we show that this rhythmic patterning of activity is sufficient to promote long-term memory storage in the absence of sleep.