In a large skillet melt the butter over medium heat and add the onion and garlic. Sauté until the onions are soft and translucent about 1 to 2 minutes. Add the chicken, sprinkle with salt and pepper and cook for about 5-6 minutes, until the chicken is cooked through.
Sprinkle the flour over the onions and chicken and stir to combine. Cook over medium heat for one minute. Slowly whisk in the chicken broth and milk. Bring the sauce to a simmer over medium to medium-high heat, while stirring the sauce continuously with the whisk. Simmer until the sauce has thickened, about 5 minutes. Taste and add more salt and pepper, if needed.
Serve the chicken sauce over rice with your toppings of choice. My family loves chow mien noodles, pineapple tidbits, cheddar cheese, tomatoes, green bell pepper, almond slices, green onions, and coconut.