Globular clusters (GCs) are dense, gravitationally bound systems of thousands to millions of stars. They are preferentially associated with the oldest components of galaxies, and measurements of their composition can therefore provide insight into the build-up of the chemical elements in galaxies in the early Universe. We report a massive GC in the Andromeda Galaxy (M31) that is extremely depleted in heavy elements. Its iron abundance is about 800 times lower than that of the Sun, and about three times lower than in the most iron-poor GCs previously known. It is also strongly depleted in magnesium. These measurements challenge the notion of a metallicity floor for GCs and theoretical expectations that massive GCs could not have formed at such low metallicities.