Combine cornstarch and water in a medium bowl, stirring until smooth. Add coconut milk and next 8 ingredients, stirring well. Set aside.
Heat 1/2 tablespoon oil in a large, deep nonstick skillet over medium-high heat. Add chicken to pan; sauté 5 minutes or until done. Remove chicken from pan, and set aside. Add remaining 1/2 tablespoon oil to pan.
Add peas and next 3 ingredients to pan; sauté 3 minutes or just until crisp-tender. Stir in coconut milk mixture. Bring to a boil over medium-high heat; cook 3 to 4 minutes or until thick. Return chicken to pan; cook 1 to 2 minutes or until chicken is thoroughly heated.
Spoon chicken mixture into bowls; top with peanuts, cilantro, and lime wedges. Serve immediately with rice.