The interstellar material from which the solar system formed has been modified by many processes: evaporation and condensation in the solar nebula, accretion into protoplanetary bodies and post-accretion processes within these bodies. Meteorites provide a record of these events and their chronology. Carbonaceous CI chondrites are among the most primitive, undifferentiated meteorites, but nevertheless show evidence of post-accretion alteration; they contain carbonates that are believed to have formed by reactions between anhydrous CI precursor materials and circulating fluids in the meteorite parent body (or bodies), yet little is known about the nature of these reactions or the timescale on which they occurred. Here we report measurements of excess 53Cr--formed by the decay of short-lived 53Mn--in five carbonate fragments from the CI chondrites Orgueil and Ivuna. Our results show that aqueous alteration on small protoplanetary bodies must have begun less than 20 Myr after the time of formation of the oldest known solar-nebula condensates (Allende refractory inclusions). This upper limit is much shorter than that of 50 Myr inferred from previous studies, and clearly establishes aqueous alteration as one of the earliest processes in the chemical evolution of the solar system.