Forming an episodic memory requires binding together disparate elements that co-occur in a single experience. One model of this process is that neurons representing different components of a memory bind to an "index"--- a subset of neurons unique to that memory. Evidence for this model has recently been found in chickadees, specialist birds that use hippocampal memory to store and recall locations of cached food. Chickadee hippocampus produces sparse, high-dimensional patterns ("barcodes") that uniquely specify each caching event. Unexpectedly, the same neurons that participate in barcodes also exhibit conventional place tuning. It is unknown how barcode activity is generated, and what role it plays in memory formation and retrieval. It is also unclear how a memory index (e.g. barcodes) could function in the same neural population that represents memory content (e.g. place). Here, we design a biologically plausible model that generates barcodes and uses them to bind experiential content. Our model generates barcodes from place inputs through the chaotic dynamics of a recurrent neural network and uses Hebbian plasticity to store barcodes as attractor states. The model matches experimental observations that barcode and place signals are randomly intermixed in the activity of single neurons. We demonstrate that barcodes reduce memory interference between correlated experiences. We also show that place tuning plays a complementary role to barcodes, enabling flexible, contextually-appropriate memory retrieval. Finally, we show how our model is compatible with previous models of the hippocampus as a predictive map. Our results suggest how the hippocampus may use barcodes to resolve fundamental tensions between memory specificity (pattern separation) and flexible recall (pattern completion) in general memory systems.