Behavior is used to assess memory and cognitive deficits in animals like Fmr1-null mice that model Fragile X Syndrome, but behavior is a proxy for unknown neural events that define cognitive variables like recollection. We identified an electrophysiological signature of recollection in mouse dorsal Cornu Ammonis 1 (CA1) hippocampus. During a shocked-place avoidance task, slow gamma (SG) (30-50 Hz) dominates mid-frequency gamma (MG) (70-90 Hz) oscillations 2-3 s before successful avoidance, but not failures. Wild-type (WT) but not Fmr1-null mice rapidly adapt to relocating the shock; concurrently, SG/MG maxima (SGdom) decrease in WT but not in cognitively inflexible Fmr1-null mice. During SGdom, putative pyramidal cell ensembles represent distant locations; during place avoidance, these are avoided places. During shock relocation, WT ensembles represent distant locations near the currently correct shock zone, but Fmr1-null ensembles represent the formerly correct zone. These findings indicate that recollection occurs when CA1 SG dominates MG and that accurate recollection of inappropriate memories explains Fmr1-null cognitive inflexibility.