Cut chicken into thin bite-size strips; set aside. For sauce, in a small bowl, stir together hoisin sauce, rice vinegar, soy sauce, and crushed red pepper; set aside.
Pour 2 teaspoons of the oil into a large nonstick wok or large nonstick skillet. Heat over medium-high heat. Add ginger; cook and stir for 15 seconds. Add carrots and stir-fry for 1 minute. Add broccoli and edamame and stir-fry 4 to 5 minutes more or until vegetables are crisp-tender. Remove vegetables from wok. Add remaining 1 teaspoon oil to the wok. Add chicken strips and stir-fry for 2 to 4 minutes or until chicken is no longer pink. Return vegetables to the wok. Add sauce to chicken mixture, tossing to coat. Heat through.
Meanwhile, heat rice according to package directions. Serve chicken mixture over rice.