A theory for the calculation of nuclear magnetic shielding constants at the coupled-cluster singles and doubles level augmented by a perturbative correction for connected triple excitations (CCSD(T)) has been developed and implemented. The approach, which is based on the gauge-including atomic orbital (CIAO) ansatz, is illustrated by several numerical examples. These include a comparison of CCSD(T) and other highly correlated methods with full configuration interaction for the BH molecule, and a systematic comparison with experiment for HF, H2O, NH3, CH4, N-2, CO, HCN, and F-2. The results demonstrate the importance of triple excitations in establishing quantitative accuracy. Finally, the ability of GIAO-CCSD(T) to make accurate predictions for difficult cases is explored in calculations for formaldehyde (CH2O), diazomethane (CH2NN), and ozone (O-3).