Arrange chicken between 2 sheets of plastic wrap; pound to an even thickness with a meat mallet or small, heavy skillet.
Sprinkle chicken with ⅜ teaspoon salt and ¼ teaspoon black pepper.
Heat a grill pan over medium-high heat.
Add chicken to the pan, and grill until cooked through, 7–8 minutes per side.
Meanwhile, combine the peaches, onions, jalapeño, lime zest, and remaining ⅛ teaspoon salt and ¼ teaspoon black pepper.
Serve salsa over chicken.
