The magnetic structure of Cr films deposited on single crystal Fe(001)/GaAs(001) substrates is investigated by soft x-ray magnetic circular dichroism (SXMCD) of the L2 and L3 absorption edges. We find that 0.25 ML Cr coverages result in Cr moments aligned with each other and antialigned to the underlying Fe moment direction. The Cr moment is measured to be 0.6±0.2 μB. Additional Cr deposition results in a monotonically reducing averaged moment consistent with the island growth of ferromagnetic Cr sheets of a single layer, antialigned with adjoining sheets. SXMCD measurements of the trilayer structures clearly show the antiferromagnetic coupling of the two Fe films through the interlying Cr film.