A rare porous magnesium-based metal-organic framework, Mg-MOF-1 [Mg(3,5-PDC)(H2O)], was synthesized solvothermally in DMF. Structural determination by X-ray single-crystal diffraction technique reveals that this chiral MOF (space group P6(1)22) is constructed by helical assembly of Mg2+ ions with achiral 3,5-pyridine dicarboxylates and coordinating water molecules, to form a three-dimensional framework with parallel hexagonal channels. The structural detail of its 0D analogue Mg-MOF-2 [Mg(2,4-PDC)(H2O)(3)] has been discussed to show how subtle variation in the ligand architecture changes the resulting structure from 0D to 3D. Mg-MOF-1 remains robust and porous upon evacuation of the coordinating water molecules. This is the first report of a chiral hexagonal Mg-MOF synthesized from an achiral organic building unit. Open Mg metal sites show selective hydrogen (H-2) adsorption (ca. 0.8 wt% at 77 K) and carbon dioxide (CO2) uptake (ca. 0.7 mmol g(-1) at 298 K) over nitrogen at 1 atm. Ab initio quantum chemical calculation of adsorption energies and possible adsorption sites of hydrogen molecules are also reported.