Parts of the potential energy surface of the title process and related processes have been investigated at the SCF/6-31G**, SCF/6-31++G**, and MP2/6-31++G** levels. The investigated reaction is exothermic (-6.23 kcal/mol, MP4/6-31++G**//MP2/6-31++G** levels, ZPE included): A linear intermediate radical anion, Li-H-Li-H.-, is significantly stabilized with respect to LiH + LiH.- (-38.74 kcal/mol, the same level as above). The BSSE at MP2/6-31++G**//MP2/6-31++G** amounts to 1.8 kcal/mol. The title process seems to be suitable for experimental study in molecular beams.