We report a new measurement of the pseudorapidity ( $\ensuremath{\eta}$) and transverse-energy ( ${E}_{T}$) dependence of the inclusive jet production cross section in $p\overline{p}$ collisions at $\sqrt{s}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.8\mathrm{TeV}$ using $95{\mathrm{pb}}^{\ensuremath{-}1}$ of data collected with the D0 detector at the Fermilab Tevatron. The differential cross section ${d}^{2}\ensuremath{\sigma}/({\mathrm{dE}}_{T}d\ensuremath{\eta})$ is presented up to $|\ensuremath{\eta}|\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$, significantly extending previous measurements. The results are in good overall agreement with next-to-leading order predictions from QCD and indicate a preference for certain parton distribution functions.