Melt butter in small pot over medium heat. Meanwhile, mix flour, salt, & pepper in a small bowl. Pour flour mixture into melted butter & stir until thickened & well mixed.
Slowly add in chicken broth stirring & heating until well mixed & thickened.
Add in milk- stirring continuously over medium high heat (being careful not to let it boil or scorch) until mixture thickens to that of a creamy soup.
Pull off of heat & pour mixture in baking dish. Mix well with rice.
Season chicken pieces to desired taste with salt & pepper. Lay pieces over soup mixture.
Bake at 350° for 1 hour and 30 minutes -OR- until an internal temperature of 165° is reached.