We have studied the nanofriction of Ne monolayers with a quartz-crystal microbalance technique at temperatures below 6.5 K and in ultrahigh-vacuum conditions. Very homogeneous and smooth lead electrodes have been physically deposited on a quartz blank at 150 K and then annealed at room temperatures. With such a Pb-plated quartz-crystal microbalance, we have observed a pronounced depinning transition separating a low-coverage region, where the film is nearly locked to the oscillating electrode, from a high-coverage region characterized by slippage at the solid-fluid boundary. Such a behavior has been found to be very reproducible. These data are suggestive of a structural depinning of the solid Ne film when it becomes incommensurate with the lead substrate, in agreement with the results of an extensive molecular-dynamics study.