We show how the transition state wave packet method of Zhang and Light can be applied within a real wave packet formalism. We also implement random superpositions into the approach, as in the recent work of Matzkies and Manthe, which can significantly reduce the number of propagations at higher temperatures. The net result is a very efficient approach for calculating the cumulative reaction probability, and hence the thermal rate constant, for bimolecular chemical reactions. Full dimensional quantum calculations, including all relevant total angular momenta, of the cumulative reaction probability and thermal rate constant for the D + H-2--> HD + H are used as illustration. [S0021-9606(00)01205-8].