In a large skillet, heat the oil, soy sauce, and half the seasoning packet over medium heat. Add the chicken and cook, turning occasionally, until beginning to brown, 2 to 3 minutes.
Add the pepper, onion, and carrot and cook, stirring occasionally, until the vegetables are tender and the chicken is cooked through, 3 to 4 minutes.
Meanwhile, cook the noodles according to the package directions; drain. Toss with the chicken and vegetables.