We apply an anisotropic version of the polymer reference interaction site model (PRISM) integral equation description of flexible polymers to analyze athermal liquid crystallinity. The polymers are characterized by a statistical segment length, sigma(o), and by a physical hard-core thickness, d, that prevents the overlap of monomers on different chains. At small segment densities, rho, the microscopic length scale d is irrelevant (as it must be in the universal semidilute regime), but becomes important in concentrated solutions and melts. Under the influence of the excluded volume interactions alone, the chains undergo a lyotropic, first-order isotropic-nematic transition at a concentration dependent upon the dimensionless "aspect ratio," sigma(o)/d. The transition becomes weaker as d --> 0, becoming second order, as has been previously shown. We extend the theory to describe the transition of rigid, thin rods, and discuss the evolution of the anisotropic liquid structure in the ordered phase. (C) 2000 American Institute of Physics. [S0021-9606(00)51510-4].