The magnetic susceptibility of the dinuclear chromium(III) complex [(CH3CN)5CrOCr(NCCH3)5](BF4)4 · 2 CH3CN has been measured and analyzed. With a fitted value of the triplet energy J = 650 cm-1, the antiferromagnetic coupling is the strongest hitherto determined for an unsupported linear oxide-bridged dinuclear Cr(III) system. The applicability of DFT for computational prediction of exchange in strongly coupled chromium(III) dimers was examined and an optimal and accurate modeling approach was devised. By such modeling it was shown possible to reproduce experimental exchange coupling constants with small relative errors typically of less than 10 % ranging from the strongest coupled systems to systems with moderately strong couplings. A significant influence (>20%) of the chemical nature of the peripheral, non-bridging ligands on the exchange coupling was found and rationalized.