Reaction of the n = 2 Ruddlesden - Popper oxide Sr3Co2O5.80 with CaH2 yields an extended oxide-hydride phase: Sr3Co2O4.33H0.84. Neutron powder diffraction data reveal the material adopts a body-centered orthorhombic structure (Immm: a = 3.7551(5) angstrom, b = 3.7048(4) angstrom, c = 21.480(3) angstrom) in which the hydride ions are accommodated within disordered CoO1.16H0.46 layers. Low temperature neutron powder diffraction data show no evidence for long-range magnetic order, suggesting the chemical disorder in the anion lattice of the material leads to magnetic frustration.