The existing potential energy surfaces for the Li + HF system have been challenged by the experiments of Loesch, Stienkemeier, and co-workers. Here a very accurate potential energy surface has been obtained with rather rigorous theoretical methods. Methods up to full CCSDT have been pursued with basis sets as large as core correlated quintuple ζ. Reported here are the reactants, products, two transition states, and three intermediate complexes for this reaction. These reveal one previously undiscovered equilibrium geometry. The stationary point relative energies are very sensitive to level of theory. The reaction has a classical endothermicity of 2.6 kcal mol(-1). The complex Li···HF in the entrance valley lies 6.1 kcal/mol below the reactants. The expected transition state Li···H···F is bent with an angle of 72.2° and lies 4.5 kcal/mol above the reactants. The latter predicted classical barrier should be no more than one kcal/mol above the exact barrier. Not one but two product complexes lie 1.6 and 2.2 kcal/mol above reactants, respectively. Between the two product complexes, a second transition state, very broad, is found. The vibrational frequencies and zero-point vibrational energies (ZPVE) of all stationary points are reported, and significantly affect the relative energies.