The microstructure of a melt-quenched Mg₉₈Cu₁Y₁ alloy has been studied by high-resolution transmission electron microscopy (HRTEM) and high-angle annular detector dark-field scanning transmission electron microscopy (HAADF-STEM). We have found Cu- and Y-rich precipitates, which are uniformly dispersed in Mg-matrix grains. The precipitates are aligned parallel to the c-plane of the Mg-matrix crystal, and have the peculiar morphology consisting of a disk-shaped amorphous core sandwiched between 14H-typed long period stacking order (LPSO) crystals. A relatively stable supper-cooled liquid phase in an Mg-Cu-Y alloy system, and the formation and growth of the LPSO crystals from the amorphous phase are responsible for the peculiar morphology of the precipitates.