We have used X-ray magnetic circular dichroism and magnetometry to study isolated Fe@Cr core-shell nanoparticles with an Fe core diameter of 2.7 nm (850 atoms) and a Cr shell thickness varying between 1 and 2 monolayers. The addition of Cr shells significantly reduces the spin moment but does not change the orbital moment. At least two Cr atomic layers are required to stabilize a ferromagnetic/antiferromagnetic interface and generate the associated exchange bias and increase in coercivity.