To evaluate the feasibility of measuring differences in bulk composition among carbonaceous meteorite parent bodies from an asteroid or comet orbiter, we present the results of a performance simulation of an orbital gamma-ray spectroscopy (GRS) experiment in a Dawn-like orbit around spherical model asteroids with a range of carbonaceous compositions. The orbital altitude was held equal to the asteroid radius for 4.5 months. Both the asteroid gamma-ray spectrum and the spacecraft background flux were calculated using the MCNPX Monte-Carlo code. GRS is sensitive to depths below the optical surface (to ≈20-50 cm depth depending on material density). This technique can therefore measure underlying compositions beneath a sulfur-depleted (e.g., Nittler et al. 2001) or desiccated surface layer. We find that 3σ uncertainties of under 1 wt% are achievable for H, C, O, Si, S, Fe, and Cl for five carbonaceous meteorite compositions using the heritage Mars Odyssey GRS design in a spacecraft-deck-mounted configuration at the Odyssey end-of-mission energy resolution, FWHM = 5.7 keV at 1332 keV. The calculated compositional uncertainties are smaller than the compositional differences between carbonaceous chondrite subclasses.