Chiral propargylsilanes and chiral allenylsilanes have emerged as versatile building blocks for organic synthesis. However, efficient methods for preparing these organosilicon compounds are lacking. We herein report a highly enantioselective method for synthesis of chiral propargylsilanes and chiral allenylsilanes from readily available alkynyl sulfonylhydrazones. Specifically, chiral spiro phosphate dirhodium complexes were used to catalyze asymmetric insertion of alkynyl carbenes into the Si-H bonds of silanes to afford a variety of chiral propargylsilanes with excellent enantioselectivity. Subsequently, a platinum catalyst was used for stereospecific isomerization of the chiral propargylsilanes to the corresponding chiral allenylsilanes.