A systematic comparison of computer simulation data for linear hard-sphere and square-well chains with the results of single-chain integral equation is reported. The single-chain integral equation is derived from the polymer Kirkwood hierarchy for site-site or pair distribution functions. Quantities compared include radius of gyration, end-to-end distance, and internal energy. We examine chain lengths up to 1000 sites for hard-sphere chains. The radius of gyration and end-to-end distance from the theory are found to agree quantitatively with Monte Carlo simulation data. Results for square-well chains with the range lambda = 1.5 are compared with Monte Carlo and constant temperature molecular dynamics simulation data for chains having up to 64 sites. The radius of gyration and internal energy generally deviate from simulation data by about 10% for reduced temperatures greater than 1. The values of the radius of gyration at reduced temperatures below 1 are larger than those from simulations.