The modern search for life-bearing exoplanets emphasizes the potential detection of O(2) and O(3) absorption spectra in exoplanetary atmospheres as ideal signatures of biology. However, oxygenic photosynthesis may not arise ubiquitously in exoplanetary biospheres. Alternative evolutionary paths may yield planetary atmospheres tinted with the waste products of other dominant metabolisms, including potentially exotic biochemistries. This paper defines chlorinic photosynthesis (CPS) as biologically mediated photolytic oxidation of aqueous Cl(-) to form halocarbon or dihalogen products, coupled with CO(2) assimilation. This hypothetical metabolism appears to be feasible energetically, physically, and geochemically, and could potentially develop under conditions that approximate the terrestrial Archean. It is hypothesized that an exoplanetary biosphere in which chlorinic photosynthesis dominates primary production would tend to evolve a strongly oxidizing, halogen-enriched atmosphere over geologic time. It is recommended that astronomical observations of exoplanetary outgoing thermal emission spectra consider signs of halogenated chemical species as likely indicators of the presence of a chlorinic biosphere. Planets that favor the evolution of CPS would probably receive equivalent or greater surface UV flux than is produced by the Sun, which would promote stronger abiotic UV photolysis of aqueous halides than occurred during Earth's Archean era and impose stronger evolutionary selection pressures on endemic life to accommodate and utilize halogenated compounds. Ocean-bearing planets of stars with metallicities equivalent to, or greater than, the Sun should especially favor the evolution of chlorinic biospheres because of the higher relative seawater abundances of Cl, Br, and I such planets would tend to host. Directed searches for chlorinic biospheres should probably focus on G0-G2, F, and A spectral class stars that have bulk metallicities of +0.0 Dex or greater.