1. In a bowl, combine the peaches, jalapeño, lime juice and sugar.
2. In a large bowl, toss together the flour, bread crumbs, cornmeal, salt, thyme and cayenne. Put the chicken in a bowl of cool water. Remove the breast halves one at a time, let the excess water drip off and coat them thoroughly with the seasoned flour mixture.
3. Heat 1/4 cup of the oil in a large heavy skillet. Add the chicken, skinned side down, and cook over moderately high heat until golden on the bottom, about 5 minutes. Turn the breasts and add the remaining 2 tablespoons oil. Cook, turning occasionally, until the chicken is browned and cooked through, about 11 minutes longer. Serve with the peach-jalapeño salsa.