Heat olive oil in a large skillet over medium-high heat.
Add diced chicken to the skillet and cook until browned and cooked through, about 5-6 minutes. Remove from skillet and set aside.
In the same skillet, add garlic and onion. Sauté until softened, about 2-3 minutes.
Add grated carrot, shredded cabbage, and diced red bell pepper to the skillet. Cook until vegetables are tender, about 4-5 minutes.
Return cooked chicken to the skillet. Stir in soy sauce, sesame oil, and rice vinegar. Cook for an additional 2-3 minutes, allowing the flavors to blend.
Season with salt and pepper to taste. Stir in chopped green onions.
To serve, spoon the chicken and vegetable mixture onto individual butter lettuce leaves, using them as wraps.
Serve immediately and enjoy your delicious Low-Carb Cabbage and Chicken Lettuce Wraps!