By computer simulation, Dijkstra et al. [M. Dijkstra, D. Frenkel, and J. P. Hansen, J. Chem. Phys. 101, 3179 (1994)] reported the first entropy-driven polymer chain collapse in an athermal solvent. To gain a better understanding of chain collapse physics in the absence of attractive interactions, we performed on-lattice NVT Monte Carlo simulations on a single polymer chain immersed in a hard-core solvent of variable size, shape, and density. In general, solvent quality decreases with increasing solvent density and incipient chain collapse occurs at a unique critical density for a given solvent size and shape. The critical density is smaller for large solvent molecules, but solvent shape also plays a role. Unfavorable solvent-chain excluded volume (EV) interactions drive the collapse transition. The EV interaction is reduced and the solvent entropy increases when the chain collapses, but there is an accompanying and unfavorable loss of chain conformational entropy. At the transition density these opposing entropy changes are comparable in magnitude. In the special and important case where the EV interaction is chain conformation independent, no collapse is observed at any solvent density.