In recent observations with the Rossi X–Ray Timing Explorer we have detected two simultaneous quasi-periodic oscillation (QPO) peaks in the low mass X–ray binary and atoll source 4U 1735–44. The lower and higher frequency QPOs have frequencies varying between 632 and 729 Hz, and 982 and 1026 Hz, respectively. The fractional rms amplitudes are 3.7 to 8.1% and 5.0 to 5.8%. The frequency separation between the two QPOs changes from 341±7 Hz to 296±12 Hz. The inferred mass accretion rate during our observations is relatively low compared to that during the previous observations, where only a single QPO was present. There is weak evidence that the frequency of the QPOs correlates with the mass accretion rate, as observed in other binaries. Five X–ray bursts were recorded with no detectable oscillations with upper limits for the rms fraction of 4% to 13%.