Reaction of the n = 3 Ruddlesden-Popper oxychloride Sr4Mn3O7.5Cl2 with calcium hydride yields the topotactically reduced phase Sr4Mn3O6.5Cl2. The deintercalation of oxide ions from the central MnO1.5 layer of the starting phase is accompanied by a rearrangement of the anion lattice, resulting in a layer of composition MnO0.5 in the reduced material, consisting of chains of MnO4 tetrahedra connected by edge and corner sharing. Magnetization and low-temperature neutron diffraction data are consistent with antiferromagnetic coupling of manganese spins, but no long-range magnetic order is observed down to 5 K, presumably due to the large interlayer separation in the reduced phase. The influence of anion substitution on the structural selectivity of low-temperature reduction reactions is discussed.