Observations from NASA's Solar Dynamics Observatory of an unusually massive filament eruption on 7 June 2011 provide for the very first time images of a magnetic reconnection region in the solar corona. The reconnection occurs at a current sheet that forms between the erupting magnetic structure and a neighbouring active region. This scenario is supported by a numerical simulation of the eruption. Dense, cool back-flowing filament plasma is observed to be re-directed and heated in situ, producing coronal-temperature emission around the reconnection region. These results provide the first direct observational evidence that a large-scale re-configuration of the coronal magnetic field takes place during solar eruptions via the process of magnetic reconnection.