The inclusive forward jet cross section in deep inelastic e+p scattering has been measured in the region of cursive Greek chi-Bjorken, 4.5 · 10-4 to 4.5 · 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 cursive Greek chi is compared to cross sections predicted by various Monte Carlo models. An excess of forward jet production at small cursive Greek chi 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.