Resonance enhancement of coherent anti-Stokes Raman scattering due to the proximity of the laser frequencies to an electronic transition has been demonstrated for dilute solutions of diphenyloctatetrane in benzene. The Raman contribution to the third order susceptibility is shown to be complex near an electronic resonance and the resulting features of the coherent anti-Stokes Raman scattering spectra are discussed in detail. This work represents one step in the demonstration that the high signal to noise ratio, fluorescence rejection, and low average power levels of the coherent anti-Stokes Raman scattering experiment can be used to advantage in Raman studies of dilute solutions and materials of biological interest.