We have measured the concentrations of iridium and platinum in ancient metasediments from Akilia Island, southern West Greenland, to obtain the first direct constraints on the extraterrestrial mass flux at the Earth's surface before 3.8 Gyr. The lunar impact record indicates this was a time of heavy bombardment; the average lunar catering rate between 4.15 and 3.8 Gyr was elevated ~150 times the modern value. Hence, heightened Ir and Pt abundances are possible in sediments from this time. However, the observed concentrations of Ir and Pt in the Akilia metasediments are extremely low. In most samples, Ir < 3 ppt and Pt < 20 ppt. In contrast, the average modern crustal abundances of Ir and Pt are ~50 ppt and ~2 ppb, respectively. The very low concentrations observed in the Akilia metasediments (cherts and banded iron formations) can be reconciled with the lunar record by quantifying the effects of sedimentation rate on the efficiency with which the extraterrestrial mass flux is sampled. The observations are explained if rapidly accumulating sediments sampled stochastic bombardment by an impactor population governed by a power law mass distribution, such that exogenous Ir and Pt are concentrated in rare horizons. The required sedimentation rates are geologically plausible. This explanation has two consequences. First, evidence of massive impact events may be rare in sediments older than 3.8 Gyr despite heavy bombardment. Second, conditions at the Earth's surface may have been conducive for extensive accumulation of sedimentary sequences and for microbial life during most of the period 4.15--3.8 Gyr. It is possible that the Earth's surface hosted microbial habitats during most of this time if microbes living in deep-sea or deep-crustal environments survived photic zone vaporizing impacts that would have occurred every ~30 Myr. Hence, evidence of life is expected even in the earliest sedimentary sequences. ¿ 2001 American Geophysical Union