Combine the salt and pepper in a zip-top plastic bag with the chicken. Seal and shake well. Melt the butter in a large nonstick skillet over medium-high heat until bubbling. Add the chicken and cook 5 minutes per side until cooked through. Transfer to a plate and cover with foil; keep warm.
Combine the peaches, broth, shallots, and lemon zest in the skillet with the drippings. Bring to a simmer and cook 3 minutes until heated through.
Remove from heat and stir in the basil. Spoon the sauce and peaches over the chicken.
Note: If using fresh peaches, blanch them in boiling water for 1 minute. Peel, pit, and cut into 1/2-inch-thick wedges to measure 2 cups.