The linearized Poisson-Boltzmann equation is solved for a cylindrical polyion immersed in an ionic solution of specified pH and ionic strength. The boundary condition at the surface of the cylinder is determined self-consistently, so that the only input required is the density of ionizable groups on the cylinder surface and their dissociation characteristics. An expression is also derived for the free energy of the system and it is shown that the degree of dissociation calculated via the self-consistent boundary condition yields the minimum value of the free energy. Calculations are presented for parameters that are relevant to several systems of biological interest and the response of the system to changes in pH and ionic strength is discussed in detail.