According to the 'Faint Young Sun' paradox, during the late Archaean eon a Sun approximately 20% dimmer warmed the early Earth such that it had liquid water and a clement climate. Explanations for this phenomenon have invoked a denser atmosphere that provided warmth by nitrogen pressure broadening or enhanced greenhouse gas concentrations. Such solutions are allowed by geochemical studies and numerical investigations that place approximate concentration limits on Archaean atmospheric gases, including methane, carbon dioxide and oxygen. But no field data constraining ground-level air density and barometric pressure have been reported, leaving the plausibility of these various hypotheses in doubt. Here we show that raindrop imprints in tuffs of the Ventersdorp Supergroup, South Africa, constrain surface air density 2.7 billion years ago to less than twice modern levels. We interpret the raindrop fossils using experiments in which water droplets of known size fall at terminal velocity into fresh and weathered volcanic ash, thus defining a relationship between imprint size and raindrop impact momentum. Fragmentation following raindrop flattening limits raindrop size to a maximum value independent of air density, whereas raindrop terminal velocity varies as the inverse of the square root of air density. If the Archaean raindrops reached the modern maximum measured size, air density must have been less than 2.3 kg m(-3), compared to today's 1.2 kg m(-3), but because such drops rarely occur, air density was more probably below 1.3 kg m(-3). The upper estimate for air density renders the pressure broadening explanation possible, but it is improbable under the likely lower estimates. Our results also disallow the extreme CO(2) levels required for hot Archaean climates.