We have observed Bose-Einstein condensation of fermionic atom pairs in an ultracold ^$Li gas at magnetic fields above a Feshbach resonance, where no stable ^6Li_2 molecules would exist in vacuum. We accurately determine the position of the resonance to be 822+-3 G. Molecular Bose-Einstein condensates were detected after a fast magnetic field ramp, which transfers pairs of atoms at close distances into bound molecules. Condensate fractions as high as 80% were obtained. The large condensate fractions are interpreted in terms of pre-existing molecules which are stable even above the two-body Feshbach resonance due to the presence of the degenerate Fermi gas.