Step 1

Melt butter in a large skillet over medium-high heat. Season chicken pieces with 1 teaspoon salt and 1/2 teaspoon pepper.

Step 2

Place 3/4 cup flour in a shallow dish. Dredge chicken in flour, place in the skillet, and brown on all sides. Set chicken aside, and drain skillet, reserving about 1 tablespoon butter.

Step 3

Reduce skillet heat to medium-low, and stir in onions, carrots, celery, and garlic. Cook until tender, 5 minutes.

Step 4

Stir in 3 tablespoons flour, and cook 5 minutes more. Pour in chicken broth, season with cayenne pepper, and remaining salt and pepper. Bring to a boil, and reduce heat to low.

Step 5

Return chicken to the skillet, cover, and continue cooking until chicken juices run clear and gravy has thickened, about 30 minutes.