The origins of the building blocks of the Solar System can be studied using the isotopic composition of early planetary and meteoritic material. Oxygen isotopes in planetary materials show variations at the per cent level that are not related to the mass of the isotopes; rather, they result from the mixture of components having different nucleosynthetic or chemical origins. Isotopic variations reaching orders of magnitude in minute meteoritic grains are usually attributed to stellar nucleosynthesis before the birth of the Solar System, whereby different grains were contributed by different stars. Here we report the discovery of abundant silica-rich grains embedded in meteoritic organic matter, having the most extreme 18O/16O and 17O/16O ratios observed (both approximately 10(-1)) together with a solar silicon isotopic composition. Both O and Si isotopes indicate a single nucleosynthetic process. These compositions can be accounted for by one of two processes: a single exotic evolved star seeding the young Solar System, or irradiation of the circumsolar gas by high energy particles accelerated during an active phase of the young Sun. We favour the latter interpretation, because the observed compositions are usually not expected from nucleosynthetic processes in evolved stars, whereas they are predicted by the selective trapping of irradiation products.