Cut chicken breasts into bite-sized pieces, season with salt and pepper.
Heat sesame oil in a large skillet or wok over medium-high heat. Add chicken and cook until browned, about 5-7 minutes. Remove and set aside.
In the same pan, add garlic, ginger, bell pepper, and carrot. Stir-fry for 3-4 minutes until tender-crisp.
Cook the ramen noodles according to package instructions, drain and set aside.
In a small bowl, whisk together soy sauce, rice vinegar, and honey.
Add cooked chicken and ramen noodles back to the pan. Pour the sauce over the mixture, toss to coat everything evenly.
Stir-fry for an additional 2-3 minutes until everything is heated through and well combined.
Garnish with green onions and sesame seeds before serving.