The composition of the Earth's early atmosphere is a subject of continuing debate. In particular, it has been suggested that elevated concentrations of atmospheric carbon dioxide would have been necessary to maintain normal surface temperatures in the face of lower solar luminosity in early Earth history. Fossil weathering profiles, known as palaeosols, have provided semi-quantitative constraints on atmospheric oxygen partial pressure (pO2) before 2.2 Gyr ago. Here we use the same well studied palaeosols to constrain atmospheric pCO2 between 2.75 and 2.2 Gyr ago. The observation that iron lost from the tops of these profiles was reprecipitated lower down as iron silicate minerals, rather than as iron carbonate, indicates that atmospheric pCO2 must have been less than 10(-1.4) atm--about 100 times today's level of 360 p.p.m., and at least five times lower than that required in one-dimensional climate models to compensate for lower solar luminosity at 2.75 Gyr. Our results suggest that either the Earth's early climate was much more sensitive to increases in pCO2 than has been thought, or that one or more greenhouse gases other than CO2 contributed significantly to the atmosphere's radiative balance during the late Archaean and early Proterozoic eons.