We present a new methodology, called "direct ab initio dynamics," for calculations of thermal rate constants and related properties from first principles. The new method is based on full variational transition state theory plus multidimensional semiclassical tunneling transmission coefficients with the potential energy information to be calculated from an accurate level of ab initio electronic structure theory. To make this approach practical, we propose the use of a focusing technique to minimize the number of electronic structure calculations, while still preserving the accuracy of the dynamical results. We have applied this method to study detailed dynamics of the hydrogen abstraction reaction, CH4+H<->CH3+H-2, and obtained excellent agreement with the available experimental data for both the forward and reverse rate constants for a range of temperatures from 300 to 1500 K. In these calculations, the potential energy surface was calculated at the quadratic configuration interaction including single and double excitation (QCISD) level of theory using the triple-zeta plus polarizations 6-311G(d,p) basis set.