A long-standing goal in neuroscience is to perform exhaustive recording of each neuron in a functional local circuit. To achieve this goal, one promising approach is optical imaging of fluorescent calcium indicators, but typically the tens or hundreds of cells imaged simultaneously comprise only a tiny percentage of the neurons in an intact circuit. Here, we show that a recent innovation, objective-coupled planar illumination (OCPI) microscopy, permits simultaneous recording from three-dimensional volumes containing many thousand neurons. We used OCPI microscopy to record chemosensory responses in the mouse vomeronasal epithelium, for which expression of hundreds of receptor types implies high functional diversity. The implications of this diversity for sensory coding were examined using several classes of previously reported vomeronasal ligands, including sulfated steroids. A collection of just 12 sulfated steroids activated more than a quarter of the neurons in the apical vomeronasal epithelium; unexpectedly, responses were functionally organized into a modest number of classes with characteristic spatial distribution. Recording from a whole sensory system thus revealed new organizational principles.