All visual information reaching the brain is transmitted by retinal ganglion cells, each of which is sensitive to a small region of space known as its receptive field. Each of the 20 or so distinct ganglion cell types is thought to transmit a complete visual image to the brain, because the receptive fields of each type form a regular lattice covering visual space. However, within each regular lattice, individual receptive fields have jagged, asymmetric shapes, which could produce “blind spots” and excessive overlap, degrading the visual image. To understand how the visual system overcomes this problem, we used a multielectrode array to record from hundreds of ganglion cells in isolated patches of peripheral primate retina. Surprisingly, we found that irregularly shaped receptive fields fit together like puzzle pieces, with high spatial precision, producing a more homogeneous coverage of visual space than would be possible otherwise. This finding reveals that the representation of visual space by neural ensembles in the retina is functionally coordinated and tuned, presumably by developmental interactions or ongoing visual activity, producing a more precise sensory signal.