Heat oil in a large wok over medium heat; add garlic. Cook and stir until fragrant, about 3 minutes. Add onion; cook and stir until translucent, about 5 minutes. Stir in tomatoes; cook, mashing with a fork, until flesh and skin separate, about 5 minutes.
Place chicken in the wok; cook and stir until lightly browned, about 5 minutes. Pour in water. Cover and bring to a boil. Stir in tomato sauce; simmer until flavors combine, about 15 minutes.
Mix potatoes into the wok; simmer until tender, about 10 minutes. Stir in bell pepper and carrot; simmer until softened, about 5 minutes. Season with salt and pepper.