Recent analyses(1-4) of data from the NASA Kepler spacecraft(5) have established that planets with radii within 25 per cent of the Earth's (R-circle plus) are commonplace throughout the Galaxy, orbiting at least 16.5 per cent of Sun-like stars(1). Because these studies were sensitive to the sizes of the planets but not their masses, the question remains whether these Earth-sized planets are indeed similar to the Earth in bulk composition. The smallest planets for which masses have been accurately determined(6,7) are Kepler-10b (1.42R(circle plus)) and Kepler-36b (1.49R(circle plus)), which are both significantly larger than the Earth. Recently, the planet Kepler-78b was discovered(8) and found to have a radius of only 1.16R(circle plus). Here we report that the mass of this planet is 1.86 Earth masses. The resulting mean density of the planet is 5.57 g cm(-3), which is similar to that of the Earth and implies a composition of iron and rock.