A novel approach for the quantification of drug similarity is proposed, which makes use of the surface polarities, that is, conductor surface polarization charge densities sigma, as defined in the quantum chemically based conductor-like screening model for realistic solvation(COSMO-RS). The histogram of these surface polarities, the so-called sigma profiles, have been proven to be the key for the calculation of all kinds of partition and adsorption coefficients and, therefore, of relevant absorption, distribution, metabolism, and excretion parameters such as solubility, pKa, log BB, and many others. They also carry a large part of the information required for the estimation of desolvation and binding processes responsible for receptor binding and enzyme inhibition of drug molecules. Thus, a large degree of similarity with respect to the sigma profiles appears to be a necessary condition for drugs of similar physiological action. Driven by this insight, we propose a sigma-profile-based drug similarity measure COSMOsim for the detection of new bioisosteric drug candidates. In several examples, we demonstrate its statistical and pharmaceutical plausibility, its practicability for real drug research projects, and its unique independence from the chemical structure, which enables scaffold hopping in a natural way.