Solubility is a fundamental property of widespread significance. Despite its importance, its efficient and accurate prediction from first principles remains a major challenge. Here we propose a novel method to predict the solubility of molecules using a density of states (DOS) approach from classical molecular simulation. The method offers a potential route to solubility prediction for large (including drug-like) molecules over a range of temperatures and pressures, all from a modest number of simulations. The method was employed to predict the solubility of sodium chloride in water at ambient conditions, yielding a value of 3.77(5) mol kg−1. This is in close agreement with other approaches based on molecular simulation, the consensus literature value being 3.71(25) mol kg−1. The predicted solubility is about half of the experimental value, the disparity being attributed to the known limitation of the Joung–Cheatham force field model employed for NaCl. The proposed method also accurately predicted the NaCl model's solubility over the temperature range 298–373 K directly from the density of states data used to predict the ambient solubility.