Heat sesame oil in a large skillet over medium-high heat. Add onion to pan; sauté 3 minutes or until softened. Add garlic; sauté 30 seconds, stirring constantly. Add chicken; sauté 3 minutes or until chicken begins to brown.
Combine 3/4 cup water and the next 5 ingredients (through crushed red pepper), stirring with a whisk until sugar dissolves. Add water mixture to pan; bring to a boil. Add bell pepper and snow peas to pan; cook for 2 minutes or until vegetables are crisp-tender and sauce thickens. Sprinkle with nuts.