Today, ab initio molecular dynamics (AIMD) relies on the locality of one-electron density matrices to achieve linear growth of computation time with the system size, crucial in large-scale simulations. While Kohn-Sham orbitals strictly localized within predefined radii can offer substantial computational advantages over density matrices, such compact orbitals are not used in AIMD because a compact representation of the electronic ground state is difficult to find. Here, a robust method for maintaining compact orbitals close to the ground state is coupled with a modified Langevin integrator to produce stable nuclear dynamics for molecular and ionic systems. This eliminates a density matrix optimization and enables first orbital-only linear-scaling AIMD. An application to liquid water demonstrates that low computational overhead of the new method makes it ideal for routine medium-scale simulations, while its linear-scaling complexity allows us to extend first-principle studies of molecular systems to completely new physical phenomena on previously inaccessible length scales.