All motile organisms use spatially distributed chemical features of their surroundings to guide their behaviors, but the neural mechanisms underlying such behaviors in mammals have been difficult to study, largely due to the technical challenges of controlling chemical concentrations in space and time during behavioral experiments. To overcome these challenges, we introduce a system to control and maintain an olfactory virtual landscape. This system uses rapid flow controllers and an online predictive algorithm to deliver precise odorant distributions to head-fixed mice as they explore a virtual environment. We establish an odor-guided virtual navigation behavior that engages hippocampal CA1 "place cells" that exhibit similar properties to those previously reported for real and visual virtual environments, demonstrating that navigation based on different sensory modalities recruits a similar cognitive map. This method opens new possibilities for studying the neural mechanisms of olfactory-driven behaviors, multisensory integration, innate valence, and low-dimensional sensory-spatial processing.