This paper investigates the possible implications for the earth-system of a melting of the Greenland ice-sheet. Such a melting is a possible result of increased high latitude temperatures due to increasing anthropogenic greenhouse gas emissions. Using an atmosphere-ocean general circulation model (AOGCM), we investigate the effects of the removal of the ice sheet on atmospheric temperatures, circulation, and precipitation. We find that locally over Greenland, there is a warming associated directly with the altitude change in winter, and the altitude and albedo change in summer. Outside of Greenland, the largest signal is a cooling over the Barents sea in winter. We attribute this cooling to a decrease in poleward heat transport in the region due to changes to the time mean circulation and eddies, and interaction with sea-ice. The simulated climate is used to force a vegetation model and an ice-sheet model. We find that the Greenland climate in the absence of an ice sheet supports the growth of trees in southern Greenland, and grass in central Greenland. We find that the ice sheet is likely to regrow following a melting of the Greenland ice sheet, the subsequent rebound of its bedrock, and a return to present day atmospheric CO2 concentrations. This regrowth is due to the high altitude bedrock in eastern Greenland which allows the growth of glaciers which develop into an ice sheet.