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The chemical ordering and its effect on structure and elastic properties of Mg1-xScx alloys are studied by ab initio method. The MgSc alloys show strong chemical long range ordering tendency as the Sc concentration increase. The predicted martensitic phase of fully disordered alloy is hcp when the transformation occurs through the Burgers path. Chemical long range ordering could lead to a lattice distortion and results in a low symmetric orthorhombic martensitic phase, namely, there is a chemical-structural coupling in MgSc alloys. The chemical long range ordering also has strong hardening effect, the single crystalline elastic moduli C′, C44, Young’s modulus and Shear modulus are increased by 12.6%, 4.2%, 4.4% and 5% for Mg80Sc20 alloy, respectively. Electronic structure analysis showed that the additional s-d and p-d hybridization between near neighboring Mg and Sc ions in ordered phase is accounting for the elastic hardening and chemical-structural coupling in MgSc alloys.