The electronic structure of La2CuO4 has been investigated using first-principles cluster calculations and the chemical shieldings at the copper nucleus have been determined with several state-of-the-art quantum chemical methods. We have also calculated the copper shieldings for CuCl, which is often used as a reference substance for copper nuclear magnetic resonance shifts measurements, and found an appreciable paramagnetic contribution in agreement with precise measurements. The calculated chemical shift at the copper nucleus in La2CuO4 for an applied field parallel to the CuO2 planes is generally smaller than, but still in reasonable agreement with, the values derived from experiment with the assumption that the spin susceptibility vanishes at zero temperature. For the field perpendicular to the planes, the quantum chemical result is substantially smaller than the experimental data but in accord with a perturbation theoretical estimate. Inconsistencies in previous representations and interpretations of the copper magnetic shift data are pointed out and corrected.