A Monte Carlo (MC) study is made of the second virial coefficient A(2) for polymers using two freely rotating chains, each of bond angle 109degrees, with the Lennard-Jones 6-12 intramolecular and intermolecular potentials between beads in a cutoff version for the number of bonds in the chain ranging from 6 to 1000 in the Theta and good-solvent conditions. It is found that effects of chain ends on A(2) are appreciable for small molecular weight M, as was expected, and that the second virial coefficient A(2,Theta) at the Theta temperature, at which the ratio /M of the mean-square radius of gyration to M becomes a constant independent of M for very large M, remains slightly negative even for such large (but finite) M where the effects of chain ends disappear. Such behavior of A(2,Theta), which cannot be explained within the framework of the binary cluster theory, is shown to be understandable if possible effects of three-segment interactions are considered. The present MC data for A(2) (along with the previous ones for ) may then be consistently explained by the existent theory based on the helical wormlike chain model only if a minor correction is made to the theoretical A(2,Theta) in almost the same range where the effects of chain ends are appeciable. The present MC data are also compared with experimental data, and it is shown that the latter may also be similarly explained. (C) 2003 American Institute of Physics.