This report discusses the feasibility of making temperature profile measurements in the fuel preburner of the main engine of the space shuttle (SSME) using coherent anti-Stokes Raman spectroscopy (CARS). The principal thrust of the work is to identify problems associated with making CARS measurements in high temperature gas phase hydrogen at very high pressures (approx 400 atmospheres). To this end a theoretical study was made of the characteristics of the CAR spectra of H2 as a function of temperature and pressure and the accuracy with which temperatures can be extracted from this spectra. In addition the experimental problems associated with carrying out these measurements on a SSME at NSTL were identified. A conceptual design of a CARS system suitable for this work is included. Many of the results of the calculations made in this report are plotted as a function of temperature. In the course of presenting these results, it was necessary to decide whether the number of density or the pressure should be treated as a fixed parameter.