To gain insight into the thickness of the crust of Mercury, we use gravity and topography data acquired by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft to calculate geoid-to-topography ratios over the northern hemisphere of the planet. For an Airy model for isostatic compensation of variations in topography, we infer an average crustal thickness of 35 ± 18 km. Combined with the value of the radius of the core of Mercury, this crustal thickness implies that Mercury had the highest efficiency of crustal production among the terrestrial planets. From the measured abundance of heat-producing elements on the surface, we calculate that the heat production in the mantle from long-lived radioactive elements at 4.45 Ga was greater than 5.4 ×10-12W/kg. By analogy with the Moon, the relatively thin crust of Mercury allows for the possibility that major impact events, such as the one that formed the Caloris basin, excavated material from Mercury's mantle.