The zero-phonon line at 5233 \AA{} appearing in neutron-irradiated MgO has been shown by other workers to be consistent with an $E\ensuremath{\rightarrow}A$ electronic transition within a center possessing trigonal symmetry about the [111] direction. (The position of this line has previously been fixed at 5248 \AA{}. In the course of the work to be discussed in this paper, however, it was found to occur at 5233 \AA{} and will be reported accordingly.) In this work, the optical Faraday effect has been used to study this transition for temperatures in the range 1.60 to 4.22\ifmmode^\circ\else\textdegree\fi{}K. It is shown, by examination of the temperature and magnetic-field dependence of the Faraday angle, that the line at 5233 \AA{} is associated with a "spin-\textonehalf{}" paramagnetic center. The Faraday angle is shown to vary as $\frac{1}{T}$ in the range 1.81 to 4.22\ifmmode^\circ\else\textdegree\fi{}K for fields less than 10 kG. The field dependence is linear up to 40 kG at 4.22\ifmmode^\circ\else\textdegree\fi{}K, but at 1.81\ifmmode^\circ\else\textdegree\fi{}K it shows strong saturation behavior from 10 to 55 kG. It is found that the Faraday angle may be described by the relation $\ensuremath{\theta}=B$ tanh ($\frac{g\ensuremath{\beta}H}{2kT}$), with $g=1.9\ifmmode\pm\else\textpm\fi{}0.1$. Since the value of $g$ is close to that for a free electron, it appears that the electronic orbital angular momentum that is to be associated with the degenerate $E$ ground state is highly quenched. In addition, the spectral pattern of the Faraday angle is dispersionlike in nature, which is further evidence for orbital quenching. The relative sign of the rotation pattern is opposite to that of the $F$-center in CaO and MgO. Unlike the similar result for the $R$-center in the alkali halides, this inversion is indicative of a center whose spin-orbit coupling constant is positive, and on the basis of a simple molecular-orbital approach, it is consistent with a five-electron center possessing a "hole" in its ($1e$) orbital.