Place beans in a bowl, and cover with warm water. Cover and let stand 30 minutes. Drain and rinse with cold water; drain well.
Heat oil in a large nonstick skillet or wok over medium-high heat. Add onion and garlic; sauté 30 seconds. Add beans; sauté 10 seconds. Stir in the broth, soy sauce, and sugar; bring to a boil. Add broccoli and chicken; bring to a boil. Cover, reduce heat, and simmer 5 minutes or until the chicken is done, stirring occasionally.
Combine cornstarch and sherry, stirring well with a whisk. Add cornstarch mixture to chicken mixture, and bring to a boil. Cook mixture 1 minute, stirring constantly.