Precise comparisons of the fundamental properties of matter-antimatter conjugates provide sensitive tests of charge-parity-time (CPT) invariance(1), which is an important symmetry that rests on basic assumptions of the standard model of particle physics. Experiments on mesons(2), leptons(3,4) and baryons(5,6) have compared different properties of matter-antimatter conjugates with fractional uncertainties at the parts-per-billion level or better. One specific quantity, however, has so far only been known to a fractional uncertainty at the parts-per-million level(7,8): the magnetic moment of the antiproton, mu((p) over bar). The extraordinary difficulty in measuring mu((p) over bar) with high precision is caused by its intrinsic smallness; for example, it is 660 times smaller than the magnetic moment of the positron(3). Here we report a high-precision measurement of mu((p) over bar) in units of the nuclear magneton mu N with a fractional precision of 1.5 parts per billion (68% confidence level). We use a two-particle spectroscopy method in an advanced cryogenic multi-Penning trap system. Our result mu((p) over bar) = -2.7928473441(42) mu(N) (where the number in parentheses represents the 68% confidence interval on the last digits of the value) improves the precision of the previous best mu((p) over bar) measurement(8) by a factor of approximately 350. The measured value is consistent with the proton magnetic moment(9), mu((p) over bar) = 2.792847350(9) mu(N), and is in agreement with CPT invariance. Consequently, this measurement constrains the magnitude of certain CPT-violating effects(10) to below 1.8 x 10(-24) gigaelectronvolts, and a possible splitting of the protonantiproton magnetic moments by CPT-odd dimension-five interactions to below 6 x 10(-12) Bohr magnetons(11).