Toss chicken with 1 Tbsp. soy sauce. Place a large skillet over high heat. Add 1 Tbsp. oil, then onion; stir-fry until onion starts to brown, about 1 minute. Add chicken; stir-fry until cooked through, 5 to 6 minutes. Transfer mixture to a bowl. Add 1 Tbsp. oil to skillet. Stir-fry vegetables for 2 minutes. Transfer to bowl with chicken.
Add 1 Tbsp. oil, garlic and ginger to skillet; stir-fry for 30 seconds. Add rice; cook for 2 minutes. Add chicken, vegetables and remaining soy sauce; cook 1 minute longer. Serve immediately.