X-ray diffraction structures of the nucleosome core particle along with a variety of experiments are consistent with the idea that an important source of the free energy holding DNA to the superhelical ramp on the histone octamer surface is obtained from a relatively small amount of electrostatic neutralization of the DNA phosphate charge by positively charged histone groups, especially arginine residues. Here we present a theoretical analysis of a simple model that emphasizes the competition between the high degree of bending of the stiff DNA molecule required for its tight curvature on the histone octamer and the neutralization of the DNA phosphate charge by basic histone residues. Our calculation accounts for the strong influence of condensed counterions on the electrostatic interactions. We find that the minimum amount of free energy required to bend DNA into axial conformity with the superhelical ramp at physiological salt concentration can be provided by a scant 6% neutralization of the phosphate charge, in close correspondence to the stoichiometric neutralization of phosphate charge by the arginine side chain that intrudes into the inward-facing minor groove of each DNA double helical turn.