A Hanbury Brown and Twiss experiment for a beam of electrons has been reali
zed in a two-dimensional electron gas in the quantum Hall regime. A metalli
c split gate serves as a tunable beam splitter to partition the incident be
am into transmitted and reflected partial beams. In the nonequilibrium case
the fluctuations in the partial beams are shown to be fully anticorrelated
. demonstrating that fermions exclude each other. In equilibrium, the cross
-correlation of current fluctuations at two different contacts is also foun
d to be negative and nonzero, provided that a direct transmission exists be
tween the contacts.