Analysis of spectra of the quasar 3C 390.3 covering a period of over 20 yr shows that the blueshifted peak of H beta has been changing its radial velocity at an almost constant rate during this time. The radial velocity has increased by over 1500 km/s. The lower limit to the period of radial velocity changes is 210 yr. Although very long periods cannot be excluded by the radial velocity curve alone, other considerations suggest that the period is about 300 yr. If the radial velocity changes are due to orbital motion, the radius of the orbit is about 0.3 pc and the total mass of the system is about 7 * 109 solar masses. In the binary black-hole model the masses of the two holes are about 2.2 * 109 solar masses. and about 4.4 * 10**9 solar masses. A possible third peak claimed to be present in some 1974-75 spectra is shown to be an instrumental artifact. The narrowness of the displaced peaks in 3C 390.3 objects requires that the broad line region cloud motions are not governed solely by gravity. The black hole masses derived by Koratkar & Gaskell (1991) need to be increased significantly. This probably lowers accretion efficiences to less than 1% of the Eddington limit.

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