Abstract The cohesive energies of argon in its cubic and hexagonal closed packed structures are computed with an unprecedented accuracy of about 5 J mol −1 (corresponding to 0.05 % of the total cohesive energy). The same relative accuracy with respect to experimental data is also found for the face‐centered cubic lattice constant deviating by ca. 0.003 Å. This level of accuracy was enabled by using high‐level theoretical, wave‐function‐based methods within a many‐body decomposition of the interaction energy. Static contributions of two‐, three‐, and four‐body fragments of the crystal are all individually converged to sub‐J mol −1 accuracy and complemented by harmonic and anharmonic vibrational corrections. Computational chemistry is thus achieving or even surpassing experimental accuracy for the solid‐state rare gases.