We describe the discovery of a satellite in orbit about the dwarf planet (136472) Makemake. This satellite, provisionally designated S/2015 (136472) 1, was detected in imaging data collected with the Hubble Space Telescope's Wide Field Camera 3 on UTC April 27, 2015 at 7.80±0.04 magnitudes fainter than Makemake. It likely evaded detection in previous satellite searches due to a nearly edge-on orbital configuration, placing it deep within the glare of Makemake during a substantial fraction of its orbital period. This configuration would place Makemake and its satellite near a mutual event season. Insufficient orbital motion was detected to make a detailed characterization of its orbital properties, prohibiting a measurement of the system mass with the discovery data alone. Preliminary analysis indicates that if the orbit is circular, its orbital period must be longer than 12.4 days, and must have a semi-major axis ≳21,000 km. We find that the properties of Makemake's moon suggest that the majority of the dark material detected in the system by thermal observations may not reside on the surface of Makemake, but may instead be attributable to S/2015 (136472) 1 having a uniform dark surface. This "dark moon hypothesis" can be directly tested with future JWST observations. We discuss the implications of this discovery for the spin state, figure, and thermal properties of Makemake and the apparent ubiquity of trans-Neptunian dwarf planet satellites.