Scientists have discovered the first superconductive quasicrystal. The crystalline alloy Al-Zn-Mg became quasicrystalline when the Al content was reduced to 15 percent, while remaining a superconductor, with a very low critical temperature of ~0.05 K. The alloy behaved like a conventional weakly coupled superconductor, but the role of electronic states that are unique to quasicrystals (critical eigenstates) was not found. However, the existence of fractal superconductivity remains possible.