Gauge-invariant NMR chemical shifts of the C and H sites in ethanol is calculated over a variety of conformational and solvation environments using density functional methods. The effects of different exchange and correlation functionals and different basis sets are systematically explored. While there is often a good correlation between atomic charges, as calculated using population analysis techniques, and calculated chemical shifts, we show that calculated populations can only be used as a rough guide to estimating the magnitude of the chemical shift. To incorporate solvent, we use configurations sampled from a classical molecular dynamics simulation of solvated ethanol. We show that the calculated NMR chemical shift at the alcohol proton converges to the experimental result provided that a sufficient number of solvent molecules are included in the GIAO calculation. The predicted shift is in much better agreement with experiment than the shift predicted from clusters with fully optimized solvation shells because of the tendency of solvents to overbond to the alcohol proton in fully optimized configurations.