We have observed a Fermi-edge singularity in the tunneling current bet
ween a two-dimensional electron gas (2DEG) and a zero-dimensional loca
lized state. A sharp peak in the tunnel current is observed when the e
nergy of the localized state matches the Fermi energy of the 2DEG. The
peak grows and becomes sharper as the temperature is decreased to our
lowest temperature of 70 mK. We attribute the singularity to the Coul
omb interaction between the tunneling electron on the localized site a
nd the Fermi sea.