This Letter evaluates three-body triple dipole (DDD) interactions for quasi-one-dimensional phases of He, Ne, H-2, Ar, Kr and Xe confined within a bundle of nanotubes. We find a significant reduction in the pair potential well depth due to the DDD effect. We carry out ab initio calculations on linear and equilateral configurations of the H-2 trimer and find that overlap interactions do not greatly change the DDD interaction in the linear configuration when the spacing is greater than about 3 Angstrom. However, the DDD interaction alone is clearly insufficient for the triangular configurations studied.