Theoretical studies have predicted that the neutrons from the reaction $\mathrm{D}(\ensuremath{\gamma}, n)\mathrm{H}$ are polarized. At low gamma-ray energies, the polarization results from an interference between the electric and magnetic dipole transitions. We have measured the polarization of the photoneutrons produced from deuterium by the 2.75-Mev gamma rays of ${\mathrm{Na}}^{24}$. The photoneutrons were scattered from magnesium and the polarization determined from the left-right asymmetry using recent experimental results of Elwyn, Lane, and Langsdorf for the polarization-analyzing ability of magnesium. For gamma ray-neutron angles (center-of-mass) of 49.6\ifmmode^\circ\else\textdegree\fi{}, 71.8\ifmmode^\circ\else\textdegree\fi{}, 93.6\ifmmode^\circ\else\textdegree\fi{}, 114.8\ifmmode^\circ\else\textdegree\fi{}, and 135.7\ifmmode^\circ\else\textdegree\fi{}, the neutron polarizations are found to be -0.34\ifmmode\pm\else\textpm\fi{}0.05, -0.23\ifmmode\pm\else\textpm\fi{}0.06, -0.22\ifmmode\pm\else\textpm\fi{}0.06, -0.29\ifmmode\pm\else\textpm\fi{}0.05, and -0.24\ifmmode\pm\else\textpm\fi{}0.06, respectively, where positive polarization is taken to be in the direction of ${\mathrm{k}}_{\ensuremath{\gamma}}\ifmmode\times\else\texttimes\fi{}{\mathrm{k}}_{n}$. The results are in agreement with a calculation by Kramer in the effective-range approximation, assuming only dipole transitions and no noncentral forces.