Insulating particles can become highly electrified during powder handling, volcanic eruptions, and the wind-blown transport of dust, sand, and snow. Measurements in these granular systems have found that smaller particles generally charge negatively, while larger particles charge positively. These observations are puzzling since particles in these systems are generally chemically identical and thus have no contact potential difference. We show here that simple geometry leads to a net transfer of electrons from larger to smaller particles, in agreement with these observations. We integrate this charging mechanism into the first quantitative charging scheme for a granular system of identical insulators and show that its predictions are in agreement with measurements. Our theory thus seems to provide an explanation for the hitherto puzzling phenomenon of the size-dependent charging of granular systems of identical insulators.