Blot the oil stain with paper towels. Take care not to rub the spot or you might spread the stain.
Sprinkle cornstarch onto the stain and let it sit for 20 minutes. Use just enough cornstarch to blot the stain. The cornstarch will absorb the excess grease. After 20 minutes, shake the cornstarch into the trash.
Pour a small amount of heavy-duty laundry detergent on the stain. The amount you need depends on the size of the stain. Use just enough to coat the stain but no more. Laundry detergent isn't generally recommended for silk unless it's to clean a stain, so avoid using more than you need.
Gently brush the spot with a clean toothbrush. Work from the outside of the stain in toward the center to prevent the stain from spreading. Don't scrub the stain.
Lay the kimono flat and allow the detergent to soak into the fibers for 20 to 30 minutes. Don't be discouraged if the stain doesn't fade right away. The detergent requires time to work, and even if the stain doesn't begin to disappear at first, it will fade as it soaks.
Rinse the detergent out of the kimono with tepid water. Hot water may damage the silk or set the stain and cold water may not rinse the oil out completely.
Lay the kimono flat to dry. Don't dry it in a machine dryer or you may damage the fabric.