Melt 3 tablespoons of the butter in a large saucepan. Add the onions, season with salt and pepper and cook over moderate heat, stirring occasionally, until golden and tender, about 10 minutes. Add the garlic, paprika and cayenne and cook, stirring, until dark red in color, 2 minutes. Add the flour and the remaining 1 tablespoon butter and cook, stirring, for 2 minutes. Stir in the broth and sugar and cook until the sauce is thickened, about 2 minutes. Add the chicken to the sauce and bring to a simmer. Cook over medium-low heat until the chicken is tender, about 15 minutes. Stir in the heavy cream and vinegar. Taste and season with salt and pepper. Serve with crusty bread if desired!