GrIS mass variations over the past millennium are not well known. In particular, the role of natural forcing and internal variability in generating variations in the mass balance of the Greenland ice sheet has not been established. Until these natural climate variations are understood, it will be difficult to anticipate what role anthropogenic greenhouse gases have on GrIS-induced sea level rise. In order to address these issues, we have performed a suite of global, atmosphere-ocean general circulation model simulations of the past millennium to establish the connection between Arctic climate conditions and temperature and precipitation changes over the Greenland ice sheet. Over this period, we have examined how temperatures and precipitation over the Greenland ice sheet have varied with volcanic aerosol loading, total solar irradiance changes, Arctic sea ice extent, the North Atlantic Oscillation Index, the Atlantic Meridional Overturning Circulation, the Atlantic Multi-decadal Oscillation, the El Nino-Southern Oscillation, the Pacific North American pattern and the Eastern Atlantic pattern. I will present an analysis of the variability in these features and how they are connected to Greenland conditions in our simulations.