A theoretical formulation is presented for the dissociation of aromatic radical anions in solution, [Ar-X].(-) --> Ar. + X-, and applied to the dissociation of the p-cyanochlorobenzene radical anion [CN-Phi-Cl].(-) in several solvents. Key ingredients of the description are (i) the inclusion of the conical intersection (CI) aspects of the problem and (ii) the incorporation of nonequilibrium solvation (within a dielectric continuum solvent description). The Cl feature is critical for this cleavage in the ground electronic state, because the required electronic coupling that allows the dissociation vanishes for a planar molecular geometry but is finite for finite C-Cl bending angle. The nonequilibrium solvation aspect is required, because of the inability of the solvent to equilibrate instantly to the changing molecular charge distribution during the radical anion dissociation process. These features are illustrated via the [CN-Phi-Cl].(-) dissociation reaction path in a dimethylformamide (DMF) solvent, where C-Cl out-of-plane bending is required to avoid the Cl intersection point, which leads to a bent transition state, and where the solvent is shown to reorganize prior to the crossing of the transition state. Reaction rate constants calculated via transition state theory (TST) are in reasonable agreement with experimental values in several solvents. It is also found that intrinsic activation free energies vary linearly with the homolytic bond dissociation energy of the radical anion, which is an experimentally observed feature. Comparison with previous descriptions is given, and inclusion of the Cl features of the dissociation is shown to lead to large differences in the reaction activation free energy, which is related to the large electronic coupling, and the energetic cost to bend the C-Cl angle to reach the bent transition state. Possible improvements of the treatment, as well as extensions to other reaction problems, are discussed. Several of the theoretical constructs required for the reaction rate constants and reaction paths implemented in the present paper are developed in the second paper of this series, On the Dissociation of Aromatic Radical Anions in Solution. 2. Reaction Path and Rate Constant Analysis.