  The inclusive forward jet cross section in deep inelastic $e^+p$ scattering
has been measured in the region of $x$--Bjorken, ~$4.5 \cdot 10^{-4}$~ to ~$4.5
\cdot 10^{-2}$. This measurement is motivated by the search for effects of
BFKL--like parton shower evolution. The cross section at hadron level as a
function of \xbj is compared to cross sections predicted by various Monte Carlo
models. An excess of forward jet production at small \xbj is observed, which is
not reproduced by models based on DGLAP parton shower evolution. The Colour
Dipole model describes the data reasonably well. Predictions of perturbative
QCD calculations at the parton level based on BFKL and DGLAP parton evolution
are discussed in the context of this measurement.
