Saute the onions in butter until soft. Combine with the other ingredients (except chicken) and mix well. Season highly. Place each breast skin side up on a board. Trim away excess fat. Loosen skin from 1 side of breast and stuff approximately one third cup of the filling under the skin. Tuck the skin and meat under breast, forming an even, round, dome shape.
Put the stuffed breasts in a buttered Pyrex or metal baking dish. Fifteen minutes before baking, preheat over to 180ºC (175 C). Bake breasts until golden brown, about 30 to 35 minutes. Don't overcook or chicken will be dry. Cool slightly before serving, and cool to room temperature if you are going to slice into smaller serving pieces. Arrange on platters and decorate with fresh herbs.