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For many decades, it has been known that rhenium imparts a tremendous resistance to creep to the nickel-based high-temperature alloys colloquially known as superalloys. This effect is so pronounced that is has been dubbed "the rhenium effect." Its origins are ill-understood, even though it is so critical to the performance of these high-temperature alloys. In this paper we show that the currently known phase diagram is inaccurate, and neglects a stoichiometric compound at 20 at.% Re (Ni sub(4)Re). The presence of this precipitate at low temperatures and the short-range ordering of Re in fcc-Ni observed at higher temperatures have important ramifications for the Ni-based superalloys. The Ni sub(4)Re compound is shown to be stable by quantum mechanical high-throughput calculations at 0 K. Monte Carlo simulations show that it is thermally persistent up to [asymptotically =] 930 K when considering configurational entropy. The existence of this compound is investigated using extended x-ray absorption fine spectroscopy on a Ni sub(96.62)Re sub(3.38) alloy.