The relatively recent (<1 b.y.) flux of asteroids and comets forming large craters on the Earth and Moon may be accurately recorded by craters with bright rays on the Moon's farside. Many previously unknown farside rayed craters are clearly distinguished in the low-phase-angle images returned by the Clementine spacecraft. Some large rayed craters on the lunar nearside are probably significantly older than 1 Ga; rays remain visible over the maria due to compositional contrasts long after soils have reached optical maturity. Most of the farside crust has a more homogeneous composition and only immature rays are visible. The size-frequency distribution of farside rayed craters is similar to that measured for Eratosthenian craters (up to 3.2 b.y.) at diameters larger than 15 km. The areal density of farside rayed craters matches that of a corrected tabulation of nearside Copernican craters. Hence the presence of bright rays due to immature soils around large craters provides a consistent time-stratigraphic basis for defining the base of the Copernican System. The density of large craters less than ~3.2 b.y. old is ~3.2 times higher than that of large farside rayed craters alone. This observation can be interpreted in two ways: (1) the average cratering rate has been constant over the past 3.2 b.y. and the base of the Copernican is ~1 Ga, or (2) the cratering rate has increased in recent geologic time and the base of the Copernican is less than 1 Ga. We favor the latter interpretation because the rays of Copernicus (800--850 m.y. old) appear to be very close to optical maturity, suggesting that the average Copernican cratering rate was ~35% higher than the average Eratosthenian rate. Other lines of evidence for an increase in the Phanerozoic (545 Ga) cratering rate are (1) the densities of small craters superimposed on Copernicus and Apollo landing sites, (2) the rates estimated from well-dated terrestrial craters (≤120 m.y.) and from present-day astronomical observations, and (3) the Proterozoic rate suggested by the crater record of Australia. The hypothesis most consistent with several key observations is that the cratering rate has increased by ~2¿ during the past ~300 m.y.¿ 1997 American Geophysical Union