A method that combines the time-dependent self-consistent-held (TDSCF) method with the reaction path Hamiltonian (RPH) derived by Miller, Handy, and Adams [J. Chem. Phys. 72, 99 (1980)] is proposed. This TDSCF-RPH method allows the calculation of the real-time quantum dynamics of chemical reactions involving polyatomic molecules. When both the coupling between the normal modes and the curvature are zero, the dynamics of an F-dimensional system is shown to reduce to a one-dimensional numerical time propagation. When the reaction path curvature is zero and the coupling between the normal modes is non-zero, the dynamics is shown to still reduce to a one-dimensional problem for a specific choice of initial wavepacket (which can have an arbitrary component for the reaction coordinate), but F coupled one-dimensional equations of motion must be propagated for a general initial wavepacket (unless the RPH is transformed to the diabatic representation). When the coupling between the normal modes is zero and the reaction path curvature is non-zero but small, the dynamics is shown to reduce to a one-dimensional numerical time propagation for an arbitrary initial wavepacket. The derivations of the equations of motion for these cases are presented in this paper, and numerical tests are presented in a separate paper.