The transition path time in kinetics is the tiny fraction of an equilibrium trajectory for a single molecule when the process actually happens. It is a uniquely single molecule property, and has not yet been experimentally-determined for any system. From measurements of photon-by-photon trajectories of fluorophore-labeled single protein molecules undergoing folding and unfolding transitions, we have estimated the upper bound to be more than 104-fold less than the mean first passage time. Our estimate is consistent with a Kramers' analysis of diffusive barrier crossings.