The shape of the bedrock underneath alpine glaciers bears vital information on the erosional mechanism related to the flow of ice. So far, several geophysical exploration methods have been proposed to map the bedrock topography though with limited accuracy. Here we illustrate the first results from a technology, called cosmic ray muon radiography, newly applied in glacial geology to investigate the bedrock geometry beneath the Aletsch Glacier situated in the Central Swiss Alps. For this purpose we installed new cosmic muon detectors made of emulsion films at three sites along the Jungfrau railway tunnel and measured the shape of the bedrock under the uppermost part of Aletsch Glacier (Jungfraufirn). Our results constrain the continuation of the bedrock-ice interface up to a depth of 50 m below the surface, where the bedrock underneath the glacier strikes NE-SW and dips at 45 degrees +/- 5 degrees. This documents the first successful application of this technology to a glaciated environment.