A series of structural polytypes formed in an Mg-1 at.% Zn-2 at.% Y alloy has been identified, which are reasonably viewed as long-period stacking derivatives of the hexagonal-close-packed Mg structure with alternate AB stacking of the close-packed atomic layers. Atomic-resolution Z-contrast imaging clearly revealed that the structures are long-period chemical-ordered as well as stacking-ordered; unique chemical order along the stacking direction occurs as being synchronized with a local faulted stacking of AB'C'A, where B' and C' layers are commonly enriched by Zn/Y atoms.