MOLECULES With large spins, and associated large magnetic moments, are potential building blocks for magnetic materials(1). To make such molecules, spin-carrying metal ions can be assembled into polynuclear complexes, but the coupling between the spins is usually antiferromagnetic, leading to antiparallel alignment(2). Magnetic coupling leading to parallel alignment occurs only rarely, and even then is usually too weak for the alignment to persist at ambient temperatures(3-14). Here we report the synthesis of a tetranuclear chromium hydride cluster With a ground state of non-zero spin (spin quantum number S = 7/2), in which the intramolecular magnetic coupling is so strong that the magnetic alignment is not disturbed appreciably even at room temperature. This ground state cannot be explained either by simple parallel or antiparallel alignment of spins, but can be understood in terms of antiparallel alignment of three Cr(III) moments with one Cr(II) moment, These findings indicate that hydride ligands can mediate extremely strong magnetic exchange interactions between metal ions, and that metal hydrides may therefore be promising components for the construction of molecular magnetic materials.