The noble gases have a particularly stable electronic configuration, comprising fully filled s and p valence orbitals. This makes these elements relatively non-reactive, and they exist at room temperature as monatomic gases. Pauling predicted in 1933 that the heavier noble gases, whose valence electrons are screened by core electrons and thus less strongly bound, could form stable molecules. This prediction was verified in 1962 by the preparation of xenon hexafluoroplatinate, XePtF6, the first compound to contain a noble-gas atom. Since then, a range of different compounds containing radon, xenon and krypton have been theoretically anticipated and prepared. Although the lighter noble gases neon, helium and argon are also expected to be reactive under suitable conditions, they remain the last three long-lived elements of the periodic table for which no stable compound is known. Here we report that the photolysis of hydrogen fluoride in a solid argon matrix leads to the formation of argon fluorohydride (HArF), which we have identified by probing the shift in the position of vibrational bands on isotopic substitution using infrared spectroscopy. Extensive ab initio calculations indicate that HArF is intrinsically stable, owing to significant ionic and covalent contributions to its bonding, thus confirming computational predictions that argon should form a stable hydride species with properties similar to those of the analogous xenon and krypton compounds reported before.