We extend the theory of counterion condensation from the standard representation of a locally stiff rodlike polyion as a line of discrete charges to a helical lattice of charges. The number of counterions condensing on a helix with given axial charge density is the same as on a line of the same charge density, but the electrostatic free energy is substantially less for the helix than for the line. In fact, the free energy of assembling the helical charge lattice becomes negative at higher salt concentrations, indicating electrostatic stabilization of the helix due to the mixing entropy of condensed counterions. The electrostatic persistence lengths of the line and helix subjected to locally elastic thermal bending fluctuations differ only slightly. They have the same kappa (-2) dependence as the Odijk-Skolnick-Fixman persistence length but a different prefactor. It is commonly believed that elastic bending models for the persistence length are applicable to double-helical DNA, but we point out that DNA apparently has unique mechanical properties that do not conform to the elastic model of bending. On the other hand, the helical model and its subsequent generalization to a double helix will serve as a basis for the electrostatic free energy of DNA conformational transitions.