Whisk together soy sauce, vinegar, oyster sauce, cornstarch, and sesame oil.
In a wok or large skillet, heat vegetable oil over high. Add chicken and cook until browned, 10 minutes. Add ginger, garlic, scallions, and broccoli and cook, stirring frequently, until broccoli is bright green, 3 minutes. Add 1/4 cup water, scraping up browned bits with a wooden spoon. Stir in soy sauce mixture and cook, stirring, until thickened, 1 minute. Serve warm with rice.