To investigate the chemistry and dynamics of Jupiter's Great Red Spot (GRS), the tropospheric abundances of NH3 and PH3 in the GRS are determined and compared to those of the surrounding region, the South Tropical Zone (STZ). These gases well up from deep in the atmosphere, and, in the upper troposphere, are depleted by condensation (in the case of NH3), chemical reactions, and UV photolysis. At Jupiter's tropopause, the chemical lifetimes of NH3 and PH3 are comparable to the time constant for vertical transport over the atmospheric scale height. The distributions of these gases are therefore diagnostic of the rate of vertical transport in the upper troposphere and lower stratosphere. Three groups of Voyager IRIS spectra are analyzed, two of the STZ and one of the GRS. The two groups of STZ spectra are defined on the basis of their radiances at 602 and 226 cm-1, which reflect, respectively, the temperature near 150 mbar and the cloud opacity in the 300-600 mbar region. One selection of STZ spectra is chosen to have the same radiance as does the GRS at 226 cm-1. The other STZ selection has a significantly greater radiance, indicative of reduced cloudiness. Variations in the abundances of NH3 and PH3 are determined within the STZ, as a background for our studies of the GRS. Within the uncertainty of our measurements (-55% and +75%), the PH3 mixing ratio at 600 mbar is 3 x 10(-7), the same for all three selections. The NH3 mixing ratio profile in the pressure region between 300 and 600 mbar is the same within error (-25% and +50% at 300 mbar) for both STZ selections. In the GRS, however, NH3 is significantly depleted at 300 mbar, with an abundance of 25% that derived for the STZ selections. Since the GRS is believed to be a region of strong vertical transport, our finding of a depletion of NH3 below the tropopause within the GRS is particularly unexpected. One of the STZ selections has a temperature-pressure profile similar to that of the GRS below the 300-mbar level; therefore, condensation at this level does not easily explain the low NH3 abundance in the GRS. All samples are taken at essentially the same latitude; photolysis and/or charged particle precipitation is probably not directly responsible either. The observed NH3 depletion may have a dynamical origin or result from some unidentified chemical processes at work in the GRS.