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Cut chicken into strips. Toss with 1 tablespoon cornstarch in a medium bowl. Combine remaining cornstarch, soy sauce, oyster sauce and sesame oil in small bowl. Set aside. Place all remaining ingredients within easy reach of stovetop.
Heat 2 tablespoons oil in large nonstick skillet or wok to medium-high. Add chicken and stir-fry 5 minutes or until done (internal temp 170°F). Remove chicken from pan. Add remaining oil to pan; bring to medium-high. Add asparagus, bell pepper, onion and garlic to pan; stir-fry 1 minute. Add broth to pan; cover and cook 4 minutes or until vegetables are crisp-tender. Return chicken to pan. Add water chestnuts. Stir cornstarch sauce mixture and add to chicken and vegetable in pan. Cook 1 minute or until sauce thickens.