Spin-driven ordering of Cr in an equiatomic fcc NiFeCrCo high entropy alloy (HEA) was predicted by first-principles calculations. Ordering of Cr is driven by the reduction in energy realized by surrounding anti-ferromagnetic Cr with ferromagnetic Ni, Fe, and Co in an alloyed L12 structure. The fully Cr-ordered alloyed L12 phase was predicted to have a magnetic moment that is 36% of that for the magnetically frustrated random solid solution. Three samples were synthesized by milling or casting/annealing. The cast/annealed sample was found to have a low temperature magnetic moment that is 44% of the moment in the milled sample, which is consistent with theoretical predictions for ordering. Scanning transmission electron microscopy measurements were performed and the presence of ordered nano-domains in cast/annealed samples throughout the equiatomic NiFeCrCo HEA was identified.