The second virial coefficient, B2, has been calculated for square-well chain molecules of lengths n = 2-50 and well widths of lambda = 0.25-1.0 by Monte Carlo integration. The theta temperature, at which B2 = 0, is independent of chain length around lambda = 0.5, increases with chain length for lambda > 0.5, and decreases with chain length for lambda < 0.5. A scaling relation, T(theta)*(n)-T(theta)*(infinity) is-proportional-to n(-phi), accurately describes the departure of the theta temperature from the infinite chain length value for lambda greater-than-or-equal-to 0.6. A closed-form expression for the second virial coefficient of square-well chains is presented which accurately fits the Monte Carlo data for n = 2-50 and lambda = 0.25-0.75. When compared to the Monte Carlo results, the second virial coefficient predicted by the generalized Flory-dimer theory for square-well chains is found to be increasingly inaccurate as chain length increases. If we correct the generalized Flory-dimer equation of state by forcing it to have the correct second virial coefficient, the compressibility factor is accurately predicted at densities below eta = 0.04.