During the Last Interglacial period (~ 130-115 thousand years ago) the Arctic climate was warmer than today, and global mean sea level was probably more than 6.6 m higher. However, there are large discrepancies in the estimated contributions to this sea level change from various sources (the Greenland and Antarctic ice sheets and smaller ice caps). Here, we determine probabilistically the likely contribution of Greenland ice sheet melt to Last Interglacial sea level rise, taking into account ice sheet model parametric uncertainty. We perform an ensemble of 500 Glimmer ice sheet model simulations forced with climatologies from the climate model HadCM3, and constrain the results with palaeodata from Greenland ice cores. Our results suggest a 90% probability that Greenland ice melt contributed at least 0.6 m, but less than 10% probability that it exceeded 3.5 m, a value which is lower than several recent estimates. Many of these previous estimates, however, did not include a full general circulation climate model that can capture atmospheric circulation and precipitation changes in response to changes in insolation forcing and orographic height. Our combined modelling and palaeodata approach suggests that the Greenland ice sheet is less sensitive to orbital forcing than previously thought, and it implicates Antarctic melt as providing a substantial contribution to Last Interglacial sea level rise. Future work should assess additional uncertainty due to inclusion of basal sliding and the direct effect of insolation on surface melt. In addition, the effect of uncertainty arising from climate model structural design should be taken into account by performing a multi-climate-model comparison.