Historically, time measurements have been based on oscillation frequencies in systems of particles, from the motion of celestial bodies to atomic transitions. Relativity and quantum mechanics show that even a single particle of mass m determines a Compton frequency omega(0) = mc(2)/(h) over bar, where c is the speed of light and h is Planck's constant h divided by 2 pi. A clock referenced to omega(0) would enable high-precision mass measurements and a fundamental definition of the second. We demonstrate such a clock using an optical frequency comb to self-reference a Ramsey-Borde atom interferometer and synchronize an oscillator at a subharmonic of omega(0). This directly demonstrates the connection between time and mass. It allows measurement of microscopic masses with 4 x 10(-9) accuracy in the proposed revision to SI units. Together with the Avogadro project, it yields calibrated kilograms.