A Monte Carlo (MC) study is made of the mean-square radius of gyration [S-2] and the gyration-radius expansion factor alpha(S) for the freely rotating chain of bond angle 109degrees and with the Lennard-Jones (LJ) 6-12 intramolecular potentials between beads in a cutoff version for the number n of bonds in the chain ranging from 10 to 1500 at the reduced temperature ranging from 3.6 to 8.0, which is defined as the absolute temperature multiplied by the Boltzmann constant and divided by the depth of the well of the LJ potential. It is shown that the ratio [S-2]/n approaches asymptotically a constant independent of n for very large n at the value 3.72+/-0.05 of the reduced temperature, which value is equal to the reduced Theta temperature Theta* of the MC model system, and that possible effects of chain ends on [S-2] and therefore on alpha(S) are negligibly small. Taking the values of [S-2] at Theta* as the unperturbed ones, alpha(S)(2) is evaluated from those at various reduced temperatures higher than Theta*. It is then found that the behavior of alpha(S)(2) may be well explained in the quasi-two-parameter scheme or is in good agreement with that of real experimental data. Further, the binary cluster integral for a bead in the chain is found to be much smaller in magnitude than that for a single isolated bead at reduced temperatures higher than Theta*, the result being consistent with a previous finding. (C) 2003 American Institute of Physics.