We have analyzed 17 observations of the low-mass X-ray binary and atoll source 4U 1728-34, carried out by the Rossi X-Ray Timing Explorer in 1996 and 1997. We obtain precise measurements of the frequencies of the two simultaneous kilohertz quasi-periodic oscillations (kHz QPOs) in this source. We show that the frequency separation between the two QPO, Δν, is always significantly smaller than the frequency of the nearly coherent oscillations seen in this source during X-ray bursts, even at the lowest inferred mass accretion rate, when Δν seems to reach its maximum value. We also find that Δν decreases significantly, from 349.3+/-1.7 Hz to 278.7+/-11.6 Hz, as the frequency of the lower frequency kHz QPO increases from 615 to 895 Hz. This is the first time that variations of the kHz QPO peak separation are measured in a source that shows nearly coherent oscillations during bursts.