Transiting Exoplanet Survey Satellite (TESS) observations have revealed a compact multi-planet system around the sixth-magnitude star HR 858 (TIC 178155732, TOI 396), located 32 parsecs away. Three planets, each about twice the size of Earth, transit this slightly-evolved, late F-type star, which is also a member of a visual binary. Two of the planets may be in mean motion resonance. We analyze the TESS observations, using novel methods to model and remove instrumental systematic errors, and combine these data with follow-up observations taken from a suite of ground-based telescopes to characterize the planetary system. The HR 858 planets are enticing targets for precise radial velocity observations, secondary eclipse spectroscopy, and measurements of the Rossiter-McLaughlin effect.