Comets are believed to contain some of the most primitive material in the solar system. One of the objectives of a Comet Rendezvous Asteroid Flyby mission is to study the composition of a cometary nucleus. Remote sensing gamma ray spectroscopy can be used to obtain some compositional information of surface materials but is limited in sensitivity by signal-to-noise problems. In addition, the composition of the materials below the surface may be more characteristic of the pristine cometary material. Both of these considerations have led to the design of a penetrator system that will deliver a passive gamma ray spectrometer to the comet and determine the composition of the subsurface materials. Results of calculations for a model comet (50% CI carbonaceous chondrite, 50% ices) provide data on the expected gamma ray fluxes, the minimum detectable limits, and the detection uncertainties for 35 isotopes. These results show that this technique can determine the composition of the rocky component, the composition of the icy component, and the rock-to-ice ratio of the nucleus. The data obtained from this proposed experiment should be sufficient to address some of the important questions on the early stages in the formation of the solar system.