Invariance under the charge, parity, time-reversal (CPT) transformation(1) is one of the fundamental symmetries of the standard model of particle physics. This CPT invariance implies that the fundamental properties of antiparticles and their matter-conjugates are identical, apart from signs. There is a deep link between CPT invariance and Lorentz symmetry-that is, the laws of nature seem to be invariant under the symmetry transformation of spacetime-although it is model dependent(2). A number of high-precision CPT and Lorentz invariance tests-using a co-magnetometer, a torsion pendulum and a maser, among others-have been performed(3), but only a few direct high-precision CPT tests that compare the fundamental properties of matter and antimatter are available(4-8). Here we report high-precision cyclotron frequency comparisons of a single antiproton and a negatively charged hydrogen ion (H-) carried out in a Penning trap system. From 13,000 frequency measurements we compare the charge-to-mass ratio for the antiproton (q/m)(p)- to that for the proton (q/m)(p) and obtain (q/m)(p)/(q/m)(p) - 1 - 1(69) x 10(-12). The measurements were performed at cyclotron frequencies of 29.6 megahertz, so our result shows that the CPT theorem holds at the atto-electronvolt scale. Our precision of 69 parts per trillion exceeds the energy resolution of previous antiproton-toproton mass comparisons(7,9) as well as the respective figure of merit of the standardmodel extension(10) by a factor of four. In addition, we give a limit on sidereal variations in the measured ratio of <720 parts per trillion. By following the arguments of ref. 11, our result can be interpreted as a stringent test of the weak equivalence principle of general relativity using baryonic antimatter, and it sets a new limit on the gravitational anomaly parameter of vertical bar alpha(g) - 1 vertical bar < 8.7 x 10(-7).