Cherts are pervasive in the Precambrian and their O and Si isotopic compositions have been used extensively for reconstructing seawater paleo-temperatures. However, these reconstructions are obscured by the fact that cherts exhibit, at a given age, a large isotopic (O and Si) heterogeneity at bulk and micrometer scales. This is understood as reflecting the fact that cherts are an assemblage of silica precursors having different origins, and that diagenesis and metamorphism have modified the isotopic compositions acquired during the last equilibration with seawater. To test the contributions of the different processes that control the Si isotopic composition of cherts, we developed high-precision triple Si isotope measurements by Multicollector-Inductively Coupled-Plasma Mass-Spectrometer (MC-ICP-MS). This approach allows to identify deviations from the equilibrium Si isotopic fractionation at the level of a few ppm. Triple Si isotope data combined with trace elements and O isotope data in Precambrian cherts demonstrate that three different sources of silica were involved in the formation of cherts, and that both equilibrium and kinetic isotopic fractionation took place for Si. Archean seawater is predicted to have a triple Si isotopic composition kinetically fractionated relative to bulk silicate Earth. This requires a large kinetic isotopic fractionation during hydrothermalism of the oceanic crust and appears consistent with warm oceans in the Precambrian. However more work is required on the triple isotope systematics of Si inputs and output to seawater by rivers and authigenic clays formation. Triple Si isotope variations can thus be used as a new tool to unravel the origin of cherts and of their O and Si isotopic compositions. The present evidence of kinetic isotopic fractionations for Si isotopes also implies that Si isotopes should be associated to triple O isotope for paleotemperature reconstructions.