The magnetic properties of dilute Li$_2$(Li$_{1-x}$Fe$_x$)N with $x sim 0.001$ 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 $textit{transverse}$ magnetic fields that proves the resonant character of this tunneling process. $textit{Longitudinal}$ fields, on the other hand, lift the ground-state degeneracy and destroy the tunneling condition. An increase of the relaxation time by four orders of magnitude in applied fields of only a few milliTesla reveals exceptionally sharp tunneling resonances. Li$_2$(Li$_{1-x}$Fe$_x$)N represents a comparatively simple and clean model system that opens the possibility to study quantum tunneling of the magnetization at liquid helium temperatures.