The motion of chemical bonds within molecules can be observed in real time, in the form of vibrational wavepackets prepared and interrogated through ultrafast nonlinear spectroscopy. Such nonlinear optical measurements are commonly performed on large ensembles of molecules, and as such, are limited to the extent that ensemble coherence can be maintained. Here, we describe vibrational wavepacket motion on single molecules, recorded through time-resolved, surface-enhanced, coherent anti-Stokes Raman scattering. The required sensitivity to detect the motion of a single molecule, under ambient conditions, is achieved by equipping the molecule with a dipolar nano-antenna (a gold dumbbell). In contrast with measurements in ensembles, the vibrational coherence on a single molecule does not dephase. It develops phase fluctuations with characteristic statistics. We present the time evolution of discretely sampled statistical states, and highlight the unique information content in the characteristic, early-time probability distribution function of the signal.