Unraveling the functions of the diverse neural types in any local circuit ultimately requires methods to record from most or all of its cells simultaneously. One promising approach to this goal is fluorescence imaging, but existing methods using laser-scanning microscopy (LSM) are severely limited in their ability to resolve rapid phenomena, like neuronal action potentials, over wide fields. Here we present a microscope that rapidly sections a three-dimensional volume using a thin illumination sheet whose position is rigidly coupled to the objective and aligned with its focal plane. We demonstrate that this approach allows exceptionally low-noise imaging of large neuronal populations at pixel rates at least 100-fold higher than with LSM. Using this microscope, we studied the pheromone-sensing neurons of the mouse vomeronasal organ and found that responses to dilute urine are largely or exclusively restricted to cells in the apical layer, the location of V1r-family-expressing neurons.