Isochrony is crucial to the rhythm of human music. Some neural, behavioral and anatomical traits underlying rhythm perception and production are shared with a broad range of species. These may either have a common evolutionary origin, or have evolved into similar traits under different evolutionary pressures. Other traits underlying rhythm are rare across species, only found in humans and few other animals. Isochrony, or stable periodicity, is common to most human music, but isochronous behaviors are also found in many species. It appears paradoxical that humans are particularly good at producing and perceiving isochronous patterns, although this ability does not conceivably confer any evolutionary advantage to modern humans. This article will attempt to solve this conundrum. To this end, we define the concept of isochrony from the present functional perspective of physiology, cognitive neuroscience, signal processing, and interactive behavior, and review available evidence on isochrony in the signals of humans and other animals. We then attempt to resolve the paradox of isochrony by expanding an evolutionary hypothesis about the function that isochronous behavior may have had in early hominids. Finally, we propose avenues for empirical research to examine this hypothesis and to understand the evolutionary origin of isochrony in general.