Resonance (vibrational) Raman Optical Activity (ROA) spectra of six chiral single-walled carbon nanotubes (SWCNTs) are studied by theoretical means. Calculations are performed imposing line group symmetry. Polarizability tensors, computed at the pi-electron level, are differentiated with respect to DFT normal modes to generate spectral intensities. This computational protocol yields a ROA spectrum in good agreement with the only experiment on SWCNT, available at present. In addition to the conventional periodic electric dipole operator we introduce magnetic dipole and electric quadrupole operators, suitable for conventional k-space calculations. Consequences of the complex nature of the wave function on the scattering cross section are discussed in detail. The resonance phenomenon is accounted for by the short time approximation. Involvement of fundamental vibrations in the region of the intermediate frequency modes is found to be more notable in ROA than in Raman spectra. Calculations indicate exceptionally strong resonance enhancement of SWCNT ROA signals. Resonance ROA profile of the (6,5) tube shows an interesting sign change that may be exploited experimentally for SWCNT identification.