We present results of Rossi X-Ray Timing Explorer observations of the atoll source 4U 1702-429 in the middle of its luminosity range. Kilohertz-range quasi-periodic oscillations (QPOs) were observed first as a narrow (FWHM similar to 7 Hz) peak near 900 Hz and later as a pair consisting of a narrow peak in the range of 625-825 Hz and a faint, broad (FWHM = 91 Hz) peak. When the two peaks appeared simultaneously, the separation was 333 +/- 5 Hz. Six type I thermonuclear bursts were detected, of which five exhibited almost coherent oscillations near 330 Hz, which makes 4U 1702-429 only the second source to show burst oscillations very close to the kilohertz QPO separation frequency. The energy spectrum and color-color diagram indicate that the source executed variations in the range between the "island" and "lower banana" atoll states. In addition to the kilohertz variability, oscillations at similar to 10, similar to 35, and 80 Hz were also detected at various times, superposed on a red noise continuum. The centroid of the similar to 35 Hz QPO tracks the frequency of the kilohertz oscillation when they were both present. A Lense-Thirring gravitomagnetic precession interpretation appears more plausible in this case, compared with other atoll sources with low-frequency QPOs.