A period of sleep over the first few hours following single-trial contextual fear conditioning (CFC) is essential for hippocampally-mediated memory consolidation. Recent studies have uncovered intracellular mechanisms required for memory formation that are affected by post-conditioning sleep and sleep deprivation. However, almost nothing is known about the circuit-level activity changes during sleep that underlie activation of these intracellular pathways. Here we continuously record neuronal activity from the CA1 region of freely-behaving mice to characterize neuronal and network activity changes occurring during active memory consolidation. C57BL/6J mice were implanted with custom stereotrode recording arrays to monitor activity of individual CA1 neurons, local field potentials (LFPs), and electromyographic activity. Sleep architecture and state-specific CA1 activity patterns were assessed during a 24 h baseline recording period, and for 24 h following either single-trial CFC or Sham conditioning. We find that consolidation of CFC is not associated with significant sleep architecture changes, but is accompanied by long-lasting increases in CA1 neuronal firing, as well as increases in delta, theta, and gamma-frequency CA1 LFP activity. These changes occurred in both sleep and wakefulness, and may drive synaptic plasticity within the hippocampus during memory formation. We also find that functional connectivity within the CA1 network, assessed through functional clustering analysis (FCA) of spike timing relationships among recorded neurons, becomes more stable during consolidation of CFC. This increase in network stability was not present following Sham conditioning, was most evident during post-CFC slow wave sleep, and was negligible during post-CFC wakefulness. Thus in the interval between encoding and recall, slow wave sleep may stabilize the hippocampal contextual fear memory trace by promoting CA1 network stability.