Combine 1 Tbsp. soy sauce, 1 Tbsp. cornstarch, 1/2 teaspoon sugar and garlic; stir in chicken. Let stand 15 minutes.
Meanwhile, blend remaining 2 Tbsp. soy sauce, 1 Tbsp. cornstarch, 2 teaspoons sugar and vinegar with 3/4 cup water.
Remove flowerets from broccoli; cut into bite-size pieces. Peel stalks; cut diagonally into thin slices.
Heat 1 Tbsp. oil in hot wok or large skillet over high heat. Add chicken and stir-fry 3 minutes; remove.
Heat remaining 1 Tbsp. oil in same pan. Add broccoli, onion, carrot and red pepper; stir-fry 3 minutes. Add snow peas; stir-fry 2 minutes longer. Stir in chicken and soy sauce mixture. Cook, stirring, until sauce boils and thickens