The temperature dependence of the compressive deformation behavior of the Mg88Zn7Y5 alloy with a high volume fraction (~85%) of the long-period stacking-ordered (LPSO) phase was studied by in-situ synchrotron radiation diffraction. The as-extruded microstructure exhibits a fully recrystallized α-Mg phase with a nearly random texture. The LPSO phase, identified as the 18R polytype, is represented by wavy lamellae elongated along the extrusion direction and has an intensive basal texture. The alloy compressed along the extrusion direction at room temperature shows a superior yield strength of 480 MPa. With increasing deformation temperature, the yield strength is reduced by 15% at 200 °C and by 46% at 300 °C, respectively. At all tested temperatures, the basal slip is activated in the α-Mg matrix far below the yield strength. The macroscopic yielding of the alloy is controlled by the activation of deformation kinking in the LPSO phase. The synchrotron radiation diffraction data indicate the stress localization at kinks with respect to the grains having the same orientation.