The magnetic properties of dilute Li-2(Li1-xFex)N with x similar to 0.001 are dominated by the spin of single, isolated Fe atoms. Below T = 10 K the spin-relaxation times become temperature independent indicating a crossover from thermal excitations to the quantum tunneling regime. We report on a strong increase of the spin-flip probability in transverse magnetic fields that proves the resonant character of this tunneling process. Longitudinal fields, on the other hand, lift the ground-state degeneracy and destroy the tunneling condition. An increase of the relaxation time by 4 orders of magnitude in applied fields of only a few milliTesla reveals exceptionally sharp tunneling resonances. Li-2(Li1-xFex)N represents a comparatively simple and clean model system that opens the possibility to study quantum tunneling of the magnetization at liquid helium temperatures.