We measured the He and Ne concentrations of 50 individual extraterrestrial chromite grains recovered from mid-Ordovician (lower Darriwilian) sediments from the Lynna River section near St. Petersburg, Russia. High concentrations of solar wind-like He and Ne found in most grains indicate that they were delivered to Earth as micrometeoritic dust, while their abundance, stratigraphic position and major element composition indicate an origin related to the L chondrite parent body (LCPB) break-up event, 470 Ma ago. Compared to sediment-dispersed extraterrestrial chromite (SEC) grains extracted from coeval sediments at other localities, the grains from Lynna River are both highly concentrated and well preserved. As in previous work, in most grains from Lynna River, high concentrations of solar wind-derived He and Ne impede a clear quantification of cosmic-ray produced He and Ne. However, we have found several SEC grains poor in solar wind Ne, showing a resolvable contribution of cosmogenic 21Ne. This makes it possible, for the first time, to determine robust cosmic-ray exposure (CRE) ages in these fossil micrometeorites, on the order of a few hundred-thousand years. These ages are similar to the CRE ages measured in chromite grains from cm-sized fossil meteorites recovered from coeval sediments in Sweden. As the CRE ages are shorter than the orbital decay time of grains of this size by Poynting-Robertson drag, this suggests that the grains were delivered to Earth through direct injection into an orbital resonance. We demonstrate how CRE ages of fossil micrometeorites can be used, in principle, to determine sedimentation rates, and to correlate the sediments at Lynna River with the fossil meteorite-bearing sediment layers in Sweden.