Nuclear magnetic resonance is the most important form of molecular spectroscopy in chemistry and biochemistry but it is normally blind to chirality. It was predicted in 2004 that precessing nuclear spins in chiral molecules in a liquid in a strong magnetic field induce a rotating electric polarization that is of opposite sign for enantiomers. This polarization arises from the distortion of the electronic structure by the nuclear magnetic moment in the presence of the strong magnetic field and is equivalent to the linear effect of an electric field on the nuclear shielding tensor. The polarization is strongly enhanced in dipolar molecules through the partial orientation of the permanent dipole through the antisymmetric part of the nuclear magnetic shielding tensor. Alternatively, an applied electric field will induce a chirally sensitive magnetization perpendicular to the field and to the nuclear spin. Progress towards the experimental realization of chiral discrimination by NMR is assessed.