Heat oil in a wok or large skillet over medium-high heat. Add chicken and stir-fry in hot oil until browned. Add carrots, bell peppers, and garlic; cook and stir for 1 to 2 minutes.
Mix soy sauce and cornstarch together in a small bowl until well combined; pour mixture into the wok or skillet. Stir in pineapple with juice, vinegar, brown sugar, and ginger. Bring to a full boil and cook until vegetables are tender and sauce is thickened.
