Stable oxygen isotope ratios (delta(18)O) of Precambrian cherts have been used to establish much of our understanding of the early climate history of Earth and suggest that ocean temperatures during the Archaean era ( approximately 3.5 billion years ago) were between 55 degrees C and 85 degrees C (ref. 2). But, because of uncertainty in the delta(18)O of the primitive ocean, there is considerable debate regarding this conclusion. Examination of modern and ancient cherts indicates that another approach, using a combined analysis of delta(18)O and hydrogen isotopes (deltaD) rather than delta(18)O alone, can provide a firmer constraint on formational temperatures without independent knowledge of the isotopic composition of ambient waters. Here we show that delta(18)O and deltaD sampled from 3.42-billion-year-old Buck Reef Chert rocks in South Africa are consistent with formation from waters at varied low temperatures. The most (18)O-enriched Buck Reef Chert rocks record the lowest diagenetic temperatures and were formed in equilibrium with waters below approximately 40 degrees C. Geochemical and sedimentary evidence suggests that the Buck Reef Chert was formed in shallow to deep marine conditions, so our results indicate that the Palaeoarchaean ocean was isotopically depleted relative to the modern ocean and far cooler (<or=40 degrees C) than previously thought.