  We present experimental results on the tunneling into the edge of a two
dimensional electron gas (2DEG) obtained with a GaAs/AlGaAs cleaved edge
overgrown structure in a strong perpendicular magnetic field. While the 2DEG
exhibits typical fractional quantum Hall features of a very high mobility
sample, we observe the onset of a non-linear current-voltage characteristic in
the vicinity of nu=1. For filling factor nu<1 the system is consistent with a
non-Fermi liquid behavior, such as a Luttinger liquid, whereas for nu>1 we
observe an Ohmic tunneling resistance between the edge and a three dimensional
contact, typical for a Fermi liquid. Hence, at the edge, there is a transition
from a Luttinger liquid to a Fermi liquid. Finally, we show that the Luttinger
liquid exponent at a given filling factor is not universal but depends on
sample parameters.
