A long cylindrical cavity through a soft solid forms a soft microfluidic channel, or models a vascular capillary. We observe experimentally that, when such a channel bears a pressurized fluid, it first dilates homogeneously, but then becomes unstable to a peristaltic elastic instability. We combine theory and numerics to fully characterize the instability in a channel with initial radius a through an incompressible bulk neo-Hookean solid with shear modulus μ. We show instability occurs supercritically with wavelength 12.278....a when the cavity pressure exceeds 2.052....μ. In finite solids, the wavelength for peristalsis lengthens, with peristalsis ultimately being replaced by a long- wavelength bulging instability in thin-walled cylinders. Peristalsis persists in Gent strain-stiffening materials, provided the material can sustain extension by more than a factor of six. Although naively a pressure driven failure mode of soft channels, the instability also offers a route to fabricate periodically undulating channels, producing, for example, waveguides with photonic/phononic stop bands.