Place chicken breast on a large sheet of waxed or plastic; cover with another sheet; pound chicken breast to 1/4 inch thickness, remove the top sheet and season with salt and pepper.
Combine the goat cheese, lemon rind, and apple; divide the apple mixture among the chicken breast and spread the mixture evenly over half the surface of each breast; fold each breast in half and press the edges together, forming a pocket.
Sprinkle the flour onto a sheet of waxed paper.
In a small bowl combine the egg and water; In a shallow bowl, combine the bread crumbs and Parmesan cheese.
Dust each chicken breast lightly with flour and dip into egg mixture, moistening all surfaces.
Coat with bread crumb mixture, patting the crumbs gently in place. (The chicken can be prepared to this point several hours ahead; cover and refrigerate, when ready to cook, bring the chicken to room temperature).
In a large, heavy skillet, heat butter and oil over medium heat; Add chicken; cook until browned and cooked through, about 8 to 10 minutes per side, drain on paper towels and serve.