We have analyzed seventeen 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, ∆ν, 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 ∆ν seems to reach its maximum value. We also find that ∆ν 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 which shows nearly-coherent oscillations during bursts.