The electronic and vibrational contributions to the dipole moment, polarizabilities, and first hyperpolarizabilities of HArF are reported. These have been computed by using a series of systematically built basis sets and a hierarchy of computational methods. HArF has a very large first hyperpolarizability along the z axis. This has been rationalized by invoking the difference in the electronic structure between the ground and the first excited state. The argon fluorohydride has been recently derived and characterized. The present study provides complementary data for the understanding of the electronic structure of this interesting argon derivative.