Variational transition state theory with multidimensional tunneling contributions (VTST/MT) is tested against quantum mechanical rate constants for the reaction H+CH4-->H-2+CH3 at temperatures up to 1000 K. The VTST/MT method can be and has been applied to many reactions that cannot be treated by rigorous quantum dynamics methods. Studying the accuracy of VTST/MT by comparison with accurate quantal results that are becoming available for systems of increasing size is important for validating the theory. In the present study, covering a factor of five in temperature, the VTST/MT method is found to have a mean deviation from accurate quantal rate constants for a six-body reaction of only 13% and maximum deviation of only 23%.