The third virial coefficient A3 of long flexible chains with three-segment interactions is evaluated perturbatively to third order in the ternary segment cluster integral beta3 to explain the recent experimental finding on polystyrene and polyisobutylene that A3 has a positive minimum around the THETA temperature (where the second virial coefficient A2 is zero) in contrast to the prediction from the two-parameter theory. The calculation indicates that A3 near the THETA point is determined by two functions. One corresponds to the two-parameter theory, but the binary cluster integral beta2 is replaced by an effective binary cluster integral beta(e), i.e., by a linear combination of the binary and ternary cluster integrals. The other is a decreasing function of beta(e), multiplied by beta3, and it reduces to beta3 at the THETA point. The sum of these two functions is shown to give A3 a positive minimum around the THETA temperature, in accord with the experimental finding mentioned above. Thus, the experimentally observed increase in A3 with a decrease in temperature below THETA is due to a marked effect of three-segment interactions. It is also shown that the second virial coefficient, which is readily derived from the calculation of A3 up to second order in beta2 and beta3, contains no separate term dependent on beta3 and is a function of beta(e) up to at least second order. This indicates that in practice the binary cluster approximation holds for A2 of long flexible chains near THETA even when the ternary cluster contribution is not negligible.