We present the synthesis and structural characterisation of a transition metal oxide hydride, LaSrCoO_3H_0.7, which adopts an unprecedented structure in which oxide chains are bridged by hydride anions to form a two- dimensional extended network. The metal centers are strongly coupled by their bonding with both oxide and hydride ligands to produce magnetic ordering up to at least 350 K. The synthetic route is sufficiently general to allow the prediction of a new class of transition metal-containing electronic and magnetic materials.