We present tunneling data in the normal state of the electron doped cuprate
superconductor Pr2-xCexCuO4 for three different values of the doping x. Th
e normal state is obtained by applying a magnetic field greater than the up
per critical field H-c2 for T< T-c. We observe an anomalous normal state ga
p near the Fermi level. From our analysis of the tunneling data we conclude
that this is a feature of the normal state density of states. We discuss p
ossible reasons for the formation of this gap and its implications for the
nature of the charge carriers in the normal and the superconducting states
of cuprate superconductors.