The second virial coefficients B-2 of Lennard-Jones chain fluids were calculated through Monte Carlo integration as a function of chain length m (up to 48 segments) and temperature. We found that at a fixed temperature the second virial coefficient decreases with chain length. At low temperatures, the virial coefficient changes sign from positive to negative as pn increases. The simulation data also provide an estimate for the theta temperature T-Theta at which the attractive and repulsive interactions cancel each other for dilute solutions. It is found that the theta temperature T-Theta for Lennard-Jones chains with m > 32 is 4.65 independent of chain length m. A comparison of simulated values of B-2 with those evaluated from two different perturbation theories for chain fluid shows that these approximate theories underestimate the second virial coefficients of Lennard-Jones chains.