We report the first growth of a large (cm-scale) single crystal of the brownmillerite-type oxide ionic conductor Sr2Fe2O5, by the floating-zone method. Although the crystal is twinned on a microscopic scale with respect to the unit cell of the disordered oxygen-deficient perovskite from which it forms, this twinning is not complete or equivalent in all directions, and so it presents the possibility of direction-dependent measurements of conductivity and other properties. Single crystal neutron diffraction revealed a supercell with a doubled a axis, compared to the conventional lcmm model containing disordered left- and right-handed tetrahedral chains. It corresponds to the beta = 0, gamma = 1/2 case of the 12/m(0 beta gamma)0s chain-ordering modulation proposed by D'Hondt et al. on the basis of electron microscopy and electron diffraction evidence. Its observation by neutron diffraction for the first time proves that the tetrahedral chains are long-range ordered at room temperature, and in a more complex manner than the Ibm2 model, which has previously been assumed to describe local chain order. (C) 2012 Elsevier B.V. All rights reserved.