The two-dimensional Raman response function of CHCl3 is theoretically considered with interpretations of each peak in terms of the associated vibrational transition pathways. In order to numerically calculate the 2D Raman spectrum, ab initio calculations of necessary quantities, such as the first- and second-order derivatives of the molecular polarizability with respect to vibrational coordinates and cubic potential anharmonic coefficients, were carried out by using the basis set 6-311++G(2df,2pd) at the Hartree-Fock level. Quantitative comparison between the two nonlinear response functions associated with the mechanical and electronic anharmonicities shows that the 2D Raman response from the high-frequency intramolecular vibrational modes of CHCl3 is mainly determined by the mechanical (potential) anharmonicity contributions. On the other hand, it is found that the two distinctive contributions originating from the mechanical and electronic anharmonicities interfere in the low-frequency region of the 2D spectrum. Overall, it is suggested that the high-frequency 2D Raman spectrum could provide a map of the mechanical anharmonic mode couplings. We briefly discuss how the 2D Raman spectrum can be used to elucidate the potential energy hypersurface and in turn to study the intramolecular vibrational energy redistribution process.