We have searched for the v = 1 → 0 S(1) emission line of excited molecular hydrogen in galaxies identified with a complete sample of IRAS sources. The galaxies have far-infrared luminosities ≳ 3 X 1011 L⊙, and all lie in small groups or show morphological evidence for interaction. Galaxies associated with seven of the sources have emission line spectra indicative of star formation or other activity. Despite being selected for high luminosity, no galaxy in the sample shows H2 emission at the spectacular level seen in the merging system NGC 6240. However, the S(1) line is present in at least some objects in the sample, and the implied fractional luminosity in the line, ZS(1)/LFIR, is consistent with values of 1-3 X 10-5 seen in other interacting galaxies.