The interaction potential of three helium atoms in symmetric linear configurations is calculated under the Born-Oppenheimer approximation using an "exact" Green’s function quantum Monte Carlo method. The results are compared with those of "exact" quantum Monte Carlo calculations for the helium dimer and the Axilrod-Teller triple-dipole energy expression. For nearest neighbor separations of 5.6 bohrs, the equilibrium distance for a helium dimer, the corresponding trimer energy is -21.5+/-1.9 K, compared to -22.3+/-0.2 K, calculated for pairwise additive behavior. For all internuclear separations in the neighborhood of the van der Waals well (similar to 5.6 bohrs), the nonadditive contribution is found to be very small.