A molecular-thermodynamic framework is developed for phase equilibria in an aqueous system containing a charged globular protein and an oppositely charged linear polyelectrolyte. The globular protein is represented by a spherical macroion with its colons; the linear polyelectrolyte is represented by a charged hard-sphere chain (polyion) with corresponding counterions. The potential of mean force contains Coulombic interactions between macroions, polyions, and small ions; long-range dispersion attractions between protein macroions; and hydrophobic macroion-polyion and macroion-macroion associations. Analytic expressions for thermodynamic properties are obtained, and liquid-liquid phase equilibria (precipitation) are calculated for model systems. Adding polyelectrolyte to a protein solution leads to precipitation, but further addition of polyelectrolyte leads to redissolution of the protein. This destabilization-restabilization phenomenon follows from electrostatic interactions with coupled polymer adsorption. The effects on phase equilibria of protein charge, protein size, association energy between protein-polyion, polyion chain length, and polyion charge density are investigated for model systems and compared with experimental data. Brief consideration is given to fractional precipitation for binary aqueous mixtures of proteins with different charge densities.