The charging of surfaces of insulators beneath the thermal control blankets on spacecraft has been numerically simulated. Such insulators are found on wiring harnesses, bulkhead feed-throughs, component mounting hardware, tiewraps, thermal sensors, etc. These insulators are shielded from the low energy space plasma by the grounded solar blankets. It is determined that the surfaces of these insulators rise to many tens of kV in the Earth's electron belts unless sufficient conduction to the spacecraft frame is established. Secondary electron emission is not sufficient to hold the potential to low values. The dependence of charging upon insulator thickness, electron energy spectra, and material properties is investigated. This phenomena is posited as an explanation for the Spacecraft Anomalies seen on many spacecraft, and on the CRRES satellite in particular .