We report the results of the experimental and theoretical study of the magnetic anisotropy of single crystals of the Co-doped lithium nitride Li2(Li1-xCox)N with x = 0.005, 0.01, and 0.02. It was shown recently that doping of the Li3N crystalline matrix with 3d transition metal (TM) ions yields superior magnetic properties comparable with the strongly anisotropic single-molecule magnetism of rare-earth complexes. Our combined electron spin resonance (ESR) and THz spectroscopic investigations of Li2(Li1-xCox)N in a very broad frequency range up to 1.7 THz and in magnetic fields up to 16 T enable an accurate determination of the energies of the spin levels of the ground state multiplet Ŝ = 1 of the paramagnetic Co(I) ion. In particular, we find a very large zero field splitting (ZFS) of almost 1 THz (∼4 meV or 33 cm-1) between the ground-state singlet and the first excited doublet state. On the computational side, ab initio many-body quantum chemistry calculations reveal a ZFS gap consistent with the experimental value. Such a large ZFS energy yields a very strong single-ion magnetic anisotropy of easy-plane type resembling that of rare-earth ions. Its microscopic origin is the unusual linear coordination of the Co(I) ions in Li2(Li1-xCox)N with two nitrogen ligands. Our calculations also evidence a strong 3d-4s hybridization of the electronic shells resulting in significant electron spin density at the 59Co nuclei, which may be responsible for the experimentally observed extraordinary large hyperfine structure of the ESR signals. Altogether, our experimental spectroscopic and computational results enable comprehensive insights into the remarkable properties of the Li2[Li1-x(TM)x]N magnets on the microscopic level.