We present new Rossi X-Ray Timing Explorer observations of the low-mass X-ray binary 4U 1608-52 during the decay of its 1998 outburst. We detect, by a direct fast Fourier transform method, the existence of a second kilohertz quasi-periodic oscillation (kHz QPO) in its power density spectrum, which was previously only seen by means of the sensitivity-enhancing "shift and add" technique. This result confirms that 4U 1608-52 is a twin kHz QPO source. The frequency separation between these two QPOs decreased significantly, from 325.5±3.4 to 225.3±12.0 Hz, as the frequency of the lower kHz QPO increased from 470 to 865 Hz, in contradiction with a simple beat-frequency interpretation. This change in the peak separation of the kHz QPOs is closely similar to that previously seen in Scorpius X-1 but takes place at a 10 times lower average luminosity. We discuss this result within the framework of models that have been proposed for kHz QPO. Beat-frequency models where the peak separation is identified with the neutron star spin rate, as well as the explanations previously proposed to account for the similar behavior of the QPOs in Sco X-1, are strongly challenged by this result.