  We present tunneling data in the normal state of the electron doped cuprate
superconductor Pr$_{2-x}$Ce$_x$CuO$_4$ for three different values of the doping
$x$. The normal state is obtained by applying a magnetic field greater than the
upper critical field, $H_{c2}$ for $T < T_c$. We observe an anomalous normal
state gap 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 possible 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.
