Proton and ion beams open up new vistas for the curative treatment of tumors, but adequate technologies for monitoring the compliance of dose delivery with treatment plans in real time are still missing. Range assessment, meaning the monitoring of therapy-particle ranges in tissue during dose delivery (treatment), is a continuous challenge considered a key for tapping the full potential of particle therapies. In this context the paper introduces an unconventional concept of range assessment by prompt-gamma timing (PGT), which is based on an elementary physical effect not considered so far: therapy particles penetrating tissue move very fast, but still need a finite transit time - about 1-2ns in case of protons with a 5-20cm range - from entering the patient's body until stopping in the target volume. The transit time increases with the particle range. This causes measurable effects in PGT spectra, usable for range verification. The concept was verified by proton irradiation experiments at the AGOR cyclotron, KVI-CART, University of Groningen. Based on the presented kinematical relations, we describe model calculations that very precisely reproduce the experimental results. As the clinical treatment conditions entail measurement constraints (e.g. limited treatment time), we propose a setup, based on clinical irradiation conditions, capable of determining proton range deviations within a few seconds of irradiation, thus allowing for a fast safety survey. Range variations of 2mm are expected to be clearly detectable.