Thin films of chiral porphyrin J-aggregates have been studied by vibrationally and electronically doubly resonant sum frequency generation (SFG) spectroscopy. It was revealed that the chiral supramolecular structures of porphyrin aggregates in solutions were retained in the thin film samples, and their chirality was determined by using chiral vibrational SFG spectroscopy. Electronic resonance profiles of some vibrational bands in achiral and chiral SFG were different from each other, and both were distinct from electronic absorption spectra. To account for these peculiar profiles, we have proposed interference effects of Raman tensor components in achiral and chiral SFG susceptibilities, which is analogous to that of resonance Raman scattering.