The simulation of photochemical reactions requires a quantum mechanical treatment of electronic and nuclear dynamics. Most simulation approaches use the Born-Oppenheimer approximation and calculations of nonadiabatic couplings to evolve a wavefunction on a set of adiabatic electronic states. However, the use of adiabatic states present several challenges such as discontinuous surfaces, singular terms in the Hamiltonian, and double-valued boundary conditions. We present a direct dynamics approach for molecular vibronic dynamics which does not invoke the Born-Oppenheimer approximation simply by avoiding diagonalization of the electronic part of the Hamiltonian. Our approach evolves trajectories on linear combinations of configuration state function (CSF) surfaces, for which all terms in the Hamiltonian can be calculated exactly in a basis of active orbitals. By employing a diabatic propagation scheme for the orbitals, we ensure that all electronic terms vary smoothly as a function of nuclear coordinates. Using coupled-trajectory Ehrenfest dynamics, we avoid problems with basis-set completeness and decoherence while maintaining tractability for realistic molecules. We test our approach for LiH. In contrast with adiabatic electronic surfaces, we find that all CSF surfaces and couplings are smooth and integrable in the vicinity of avoided crossings. Comparisons of dynamics simulations with our approach and with adiabatic direct dynamics reveal the compromises in adiabatic approximations. Our approach performs highly accurate direct dynamics simulations at a comparable cost to conventional adiabatic-based techniques. It has the potential for further improvement with the adaptation of other electronic structure and vibronic dynamics methods.