Preheat oven to 350°F (175°C).

In a small bowl, stir together the flour, paprika, salt, and pepper. Roll the chicken breasts in the flour mixture until evenly coated. Place the coated chicken breasts in a 9x13 inch casserole dish.

In another bowl, combine the sour cream, cream of mushroom soup, and drained sliced mushrooms. Pour this mixture evenly over the chicken in the casserole dish.

Bake uncovered for 1 hour and 15 minutes, or until the chicken is cooked through and no longer pink in the center.

Remove the casserole dish from the oven and sprinkle the shredded cheddar cheese evenly over the top. Return to the oven for about 5 minutes, or until the cheese is melted and bubbly.

Garnish with fresh chopped chives, if desired, before serving.