Since the discovery of the first exoplanet we have known that other planetary systems can look quite unlike our own. However, until recently we have only been able to probe the upper range of the planet size distribution. The high precision of the Kepler space telescope has allowed us to detect planets that are the size of Earth and somewhat smaller, but no previous planets have been found that are smaller than those we see in our own Solar System. Here we report the discovery of a planet significantly smaller than Mercury. This tiny planet is the innermost of three planets that orbit the Sun-like host star, which we have designated Kepler-37. Owing to its extremely small size, similar to that of Earths Moon, and highly irradiated surface, Kepler-37b is probably a rocky planet with no atmosphere or water, similar to Mercury.