Cover chicken breast with plastic wrap and lightly pound all over until well flattened. Repeat with remaining chicken breasts.
In a shallow bowl, combine flour, salt, pepper, and paprika; coat chicken with the mixture. In a heavy skillet over medium heat, melt 2 tablespoons of the butter. Add 2 pieces of chicken and cook, turning, until golden and cooked through, about 10 minutes (refrigerate remaining chicken while cooking the first batch). Remove to a hot platter and keep warm; add remaining 1 tablespoon butter and repeat with remaining chicken then remove to the heated plate with first batch.
Over medium-low heat, stir remaining 2 tablespoons flour into drippings in skillet. Add broth ; cook and stir constantly until thickened. Strain through a mesh strainer and return to clean skillet. Add cream and grapes. Taste and add more salt if needed. Reheat gently; do not boil. Grapes should soften slightly. Stir in any juices from warm chicken. Pour sauce into a serving dish and top with the chicken.
Calories per serving: 468