We have investigated through simulation the electrostatic charging of the nucleus of Comet 67P/Churyumov–Gerasimenko during periods of weak outgassing activity. Specifically, we have modeled the surface potential and electric field at the surface of the nucleus during the initial Rosetta rendezvous at 3.5AU and the release of the Philae lander at 3AU. We have also investigated the possibility of dust acceleration and ejection above the nucleus due to electrostatic forces. Finally, we discuss these modeling results in the context of possible observations by instruments on both the Rosetta orbiter and the Philae lander.