Synthesizing half-metallic fully-compensated ferrimagnets that form in the inverse Heusler phase could lead to superior spintronic devices. These materials would have high spin polarization at room temperature with very little fringing magnetic fields. Previous theoretical studies indicated that Cr2CoAl should form in a stable inverse Heusler lattice due to its low activation energy. Here, stoichiometric Cr2CoAl samples were arc-melted and annealed at varying temperatures, followed by studies of their structural and magnetic properties. High-resolution synchrotron X-ray diffraction revealed a chemically ordered Heusler phase in addition to CoAl and Cr phases. Soft X-ray magnetic circular dichroism revealed that the Cr and Co magnetic moments are antiferromagnetically oriented leading to the observed low magnetic moment in Cr2CoAl.