A fully quantum mechanical treatment is presented of the three-body recombination process H + H + 4He → H2 + 4He for T = 1 K where measurements have recently been performed. The calculation employs accurate interatomic potentials and thermal averaging. An impulse approximation is used to obtain the most important contributions to the rate constant. Off-shell effects are found to be important and are included in the final results which are in reasonable agreement with experiment. We find that the rate of formation of ortho-H2 is substantially larger than that of para-H2. The magnetic field dependence of the recombination rate is also discussed.