Arrange broccoli in a vegetable steamer over boiling water. Cover and steam 5 to 8 minutes or until crisp-tender. Drain; transfer to a serving bowl, and keep warm.
Combine soy sauce and next 4 ingredients in a small saucepan; stir well. Bring to a boil over medium heat. Pour over broccoli. Add tomato, water chestnuts, and green onions; toss gently.