Proton nuclear magnetic resonance (NMR) shifts of aliphatic alcohols in chloroform have been computed on the basis of density functional theory, the solvent being included by the integral-equation-formalism polarisable continuum model of Gaussian 09. Relative energies of all conformers are calculated at the Perdew, Burke and Ernzerhof (PBE)0/6-311+G(d,p) level, and NMR shifts by the gauge-including atomic orbital method with the PBE0/6-311+G(d,p) geometry and the cc-pVTZ basis set. The 208 computed CH proton NMR shifts for 34 alcohols correlate very well with the experimental values, with a gradient of 1.00 ± 0.01 and intercept close to zero; the overall root mean square difference (RMSD) is 0.08 ppm. Shifts for CH protons of diols in chloroform are well correlated with the theoretical values for (isotropic) benzene, with similar gradient and intercept (1.02 ± 0.01, -0.13 ppm), but the overall RMSD is slightly higher, 0.12 ppm. This approach generally gives slightly better results than the CHARGE model of Abraham et al. The shifts of unsaturated alcohols in benzene have been re-examined with Gaussian 09, but the overall fit for CH protons is not improved, and OH proton shifts are worse. Shifts of vinyl protons in alkenols are systematically overestimated, and the correlation of computed shifts against the experimental data for unsaturated alcohols follows a quadratic equation. Splitting the 20 compounds studied into two sets, and applying empirical scaling based on the quadratic for the first set to the second set, gives an RMSD of 0.10 ppm. A multi-standard approach gives a similar result.