The terrestrial sediment record indicates that the Earth's climate varied drastically in the Precambrian era (before 550 million years ago), ranging from surface temperatures similar to or higher than today's to global glaciation events. The most continuous record of sea surface temperatures of that time has been derived from variations in oxygen isotope ratios of cherts (siliceous sediments), but the long-term cooling of the oceans inferred from those data has been questioned because the oxygen isotope signature could have been reset through the exchange with hydrothermal fluids after deposition of the sediments. Here we show that the silicon isotopic composition of cherts more than 550 million years old shows systematic variations with age that support the earlier conclusion of long-term ocean cooling and exclude post-depositional exchange as the main source of the isotopic variations. In agreement with other lines of evidence, a model of the silicon cycle in the Precambrian era shows that the observed silicon isotope variations imply seawater temperature changes from about 70 degrees C 3,500 million years ago to about 20 degrees C 800 million years ago.