We show that values of the magnetic anisotropy energy (MAE), which are about two orders of magnitude larger than the usual ones for transition metal cations in insulators (approximately 0.01-1 cm(-1)), can be found for the less common ion Fe+. In SrCl2:Fe+, the MAE is 93 cm(-1) when calculated using second-order perturbation multi-configurational calculations (CASPT2) while a similar value is found using multi-reference density functional theory (MR-DFT). This result is even larger than other recently reported giant MAEs for atoms on surfaces or magnetic clusters. The microscopic origin of this giant MAE is discussed in detail.