We report the preliminary results of an experiment designed to search for the $C$-nonconserving decay of ground-state orthopositronium ($1^{3}S_{1}$) into four photons. In terms of the branching ratio ${{F}_{T}}^{4\ensuremath{\gamma}}=\frac{{{R}_{T}}^{4\ensuremath{\gamma}}(^{3}S_{1}\ensuremath{\rightarrow}4\ensuremath{\gamma})}{{R}_{3\ensuremath{\gamma}}(^{3}S_{1}\ensuremath{\rightarrow}3\ensuremath{\gamma})}$, where ${{R}_{T}}^{4\ensuremath{\gamma}}(^{3}S_{1}\ensuremath{\rightarrow}4\ensuremath{\gamma})$ is the $C$-nonconserving four-photon decay rate and ${R}_{3\ensuremath{\gamma}}(^{3}S_{1}\ensuremath{\rightarrow}3\ensuremath{\gamma})$ is the $C$-conserving three-photon decay rate of free orthopositronium in our sample, we find ${{F}_{T}}^{4\ensuremath{\gamma}}<8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ (68% confidence).