  We present a combined experimental and theoretical study of the
self-diffusion of ammonia on exfoliated graphite. Using neutron time-of-flight
spectroscopy we are able to resolve the ultrafast diffusion process of adsorbed
ammonia, NH$_3$, on graphite. Together with van der Waals corrected density
functional theory calculations we show that the diffusion of NH$_3$ follows a
hopping motion on a weakly corrugated potential energy surface with an
activation energy of about 4 meV which is particularly low for this type of
diffusive motion. The hopping motion includes further a significant number of
long jumps and the diffusion constant of ammonia adsorbed on graphite is
determined with $D=3.9 \cdot 10^{-8}~\mbox{m}^2 /\mbox{s}$ at 94 K.
