The coherence and dephasing of vibrational motions of molecules constitute an integral part of chemical dynamics, influence material properties, and underpin schemes to control chemical reactions. In the present study, we measure coherent structural dynamics in optically excited N-methyl morpholine by scattering with ultrashort X-ray pulses from the Linac Coherent Light Source. The scattering signals are corrected for the different electron density in the excited electronic state of the molecule compared to the ground state. The experiment maps the evolution of the molecular geometry with femtosecond resolution, showing coherent motion that survives electronic relaxation and appears to persist for longer than previously seen using other methods.