We observed the low-mass X-ray binary and Z source GX 17+2 with the Rossi X-Ray Timing Explorer during 1997 February 6-8, April 1-4, and July 26-27. The X-ray color-color diagram shows a clear Z track. Two simultaneous kHz quasi-periodic oscillations (QPOs) are present in each observation, whose frequencies are well correlated with the position of the source on the Z track. At the left end of the horizontal branch (HB), only the higher frequency peak is observed, at 645 +/- 9 Hz, with an rms amplitude of 5.7% +/- 0.5% and an FWHM of 183 +/- 35 Hz. When the source moves down the Z track to the upper normal branch, the frequency of the kHz QPO increases to 1087 +/- 12 Hz, and the rms amplitude and FWHM decrease by a factor of 2. Farther down the Z track, the QPO becomes undetectable, with rms upper limits typically of 2.0%. Halfway down the HB, a second QPO appears in the power spectra with a frequency of 480 +/- 23 Hz. The frequency of this QPO also increases when the source moves along the Z track, up to 781 +/- 11 Hz halfway down the normal branch, while the rms amplitude and FWHM stay approximately constant at 2.5% and 70 Hz. The QPO frequency difference is constant at 293.5 +/- 7.5 Hz. Simultaneously with the kHz QPOs, we detect HB QPOs (HBOs). The simultaneous presence of HBOs and kHz QPOs excludes the magnetospheric beat-frequency model as the explanation for at least one of these two phenomena.