Stir together chicken broth, soy sauce, oyster sauce and cornstarch in a large cup. Set mixture aside.
Heat 1 Tbsp. oil in a 12-inch nonstick skillet over medium-high heat. Add onion, zucchini, bell pepper and bean sprouts. Cook, stirring constantly, until vegetables are crisp-tender, for about 3 minutes. Add chicken and cook for 1 minute more. Then transfer to a plate and keep warm.
Add remaining tablespoon vegetable oil and eggs to pan. Let eggs set for about 30 seconds, then scramble until they're firm, for 1 to 2 minutes. Stir reserved chicken broth mixture and pour it into pan with eggs. Stir until sauce thickens, for about 5 minutes. Add rice, chicken and vegetables to pan. Stir until blended thoroughly and heated through.