Pat chicken dry and season with salt and pepper. In a large, heavy skillet, heat oil and 1 1/2 tsp. of the butter over moderately high heat. Brown chicken in batches, two breasts at a time. Transfer to platter. In same pan, saute onion and mushrooms, stirring occassionally until liquid mushrooms gives off is evaporated. Add marsala and cook until wine is almost evaporated. Add chicken broth and chicken breasts with any juices from the plate. Simmer, turning once for 15 minutes. Transfer to clean platter. Simmer mushroom sauce until liquid is about 1/2 cup. Remove skillet from heat. Add remaining butter, stirring to incorporate. Spoon mushrooms and onons over chicken breasts.