The Curie temperature (T_c) of the iron-nickel Invar Alloy with composition 30.6 at.% Ni was studied as a function of the annealing time at different temperatures. An increase in T_c of more than 20 degrees C was observed with annealing at temperatures as low as 340 degrees C. The change in T_c with time was similar to that observed in metallic glasses, and was interpreted as an atomic rearrangement, with a change in the chemical short-range order. The activation energy for the process was estimated to be about 1.5 eV, indicating movement of quenched-in vacancies as the main relaxation mechanism.