We have discovered a new pulsating X-ray source with a 1.24-sec period in the constellation Hercules. Analysis of 5 months of data has shown the existence of periodic variations in the intensity of the source and correlated sinusoidal variations in the period of the 1.24-sec pulsations. As in the case of the pulsating X-ray source Cen X-3, we interpret this effect as due to an occulting binary system, with the intensity changes due to occultation of the X-ray source by its companion and with the sinusoidal variations in the period of the 1.24-sec pulsations due to the Doppler effect. In addition, we have observed a longer-time scale cycle in which the source is bright and pulsing for approximately 9 days during which we can observe the 1.7-day occulting, followed by approximately 27 days during which the source is not detected above background on individual 20-sec scans.