A scheme that fully exploits molecular point group symmetry in direct second-order many-body perturbation theory chemical shift calculations based on gauge-including atomic orbitals is presented and implemented. Representative calculations for the molecules B-4(Bu-t)(4) (T-d symmetry) and [AlCp](4) (D-2d symmetry) involving more than 600 basis functions demonstrate the applicability of the developed program to large symmetric molecules (which could be otherwise not treated) and indicate the importance of electron correlation effects for the reliable prediction of NMR chemical shifts in larger molecules.