Nodal chain semimetals protected by nonsymmorphic symmetries are distinct from Dirac and Weyl semimetals, featuring unconventional topological surface states and resulting in anomalous magnetotransport properties. Here, we reveal that ferromagnetic $\mathrm{FeI}{\mathrm{n}}_{2}{\mathrm{S}}_{4}$ is a suitable nodal chain candidate in theory. Centrosymmetric $\mathrm{FeI}{\mathrm{n}}_{2}{\mathrm{S}}_{4}$ with nonsymmorphic symmetries shows half metallicity and clean band crossings with hourglass-type dispersion tracing out nodal lines. Owing to glide mirror symmetries, the nontrivial nodal loops form a nodal chain, which is associated with the perpendicular glide mirror planes. These nodal chains are robust against spin-orbital interaction, giving rise to the coexistence of drumhead-type surface states and closed surface Fermi arcs. Moreover, the nodal loops protected by nonsymmorphic symmetry contribute to large anomalous Hall conductivity and the anomalous Nernst conductivity. Our results provide a platform to explore the intriguing topological state and transverse transport properties in a magnetic system.