Summary: We present the construction of an exponentially accurate time-dependent Born-Oppenheimer approximation for molecular quantum mechanics. We study molecular systems whose electron masses are held fixed and whose nuclear masses are proportional to \(\varepsilon^{-4}\), where \(\varepsilon\) is a small expansion parameter. By optimal truncation of an asymptotic expansion, we construct approximate solutions to the time-dependent Schrödinger equation that agree with exact normalized solutions up to errors whose norms are bounded by \(C\exp(-\gamma/\varepsilon^2)\), for some \(C\) and \(\gamma >0\).