An analysis of the times of minimum light for the long-period Algol-type eclipsing binary RX Gem is presented based on a new linear ephemeris. The O - C curve shows a cyclic oscillation with a period of 55.7 yr and a semiamplitude of 0.0645 day. Assuming the change to be due to the presence of a "third body" revolving around the RX Gem system, the parameters of the third body's orbit are derived. Since the third-body assumption is in good agreement with the spectroscopic data from several authors and with published photometric solutions (Gaposchkin, Hall, & Walter; Giuricin et al.), RX Gem is likely to be a triple system. In this case, the third body is an A-type star in a circular orbit, which is nearly coplanar to the orbit of the eclipsing pair. However, the recent light-curve analysis by Olson & Etzel does not show any third light, so the third star (M3 > 2.41 M⊙) may be an unseen neutron star or black hole. Additional eclipse timings over the next decade will be important to verify the presence of the third body.