We realized an equivalent Hanbury Brown and Twiss experiment for a beam of electrons in a two-dimensional electron gas in the quantum Hall regime. A metallic split gate serves as a tunable beam splitter which is used to partition the incident beam into transmitted and reflected partial beams. The current fluctuations in the reflected and transmitted beam are fully anticorrelated demonstrating that fermions tend to exclude each other (anti-bunching), If the occupation probability of the incident beam is lowered by an additional gate, the anticorrelation is reduced and disappears in the classical limit of a highly diluted beam. (C) 2000 Elsevier Science B.V. All rights reserved.