Cook spaghetti according to package directions. Heat a skillet over medium high heat and add olive oil. Cube chicken and add to a skillet. Cook until no longer pink. Chop carrots, green pepper, and garlic and add to the skillet. Cook until tender.
In a small saucepan, make your white sauce by melting 2 tablespoons of butter over medium-low heat. Add 2 tablespoons of flour and sitr until combined. Add the milk slowly, 1/2 cup at a time, getting the sauce to thicken by stirring in each half cup of milk. After sauce is creamy, combine vegetables, chicken, and sauce to the cooked noodles.