Data from recent space missions have added strong support for the idea that there are liquid oceans on several moons of the outer planets, with Jupiter's moon Europa having received the most attention. But given the extremely cold surface temperatures and meagre radiogenic heat sources of these moons, it is still unclear how these oceans remain liquid. The prevailing conjecture is that these oceans are heated by tidal forces that flex the solid moon (rock plus ice) during its eccentric orbit, and that this heat entering the ocean does not rapidly escape because of the insulating layer of ice over the ocean surface. Here, however, I describe strong tidal dissipation (and heating) in the liquid oceans; I show that a subdominant and previously unconsidered tidal force due to obliquity (axial tilt of the moon with respect to its orbital plane) has the right form and frequency to resonantly excite large-amplitude Rossby waves in these oceans. In the specific case of Europa, the minimum kinetic energy of the flow associated with this resonance (7.3 x 10(18) J) is two thousand times larger than that of the flow excited by the dominant tidal forces, and dissipation of this energy seems large enough to be a primary ocean heat source.