PEACH SALSA: Preheat a grill or grill pan to medium-high heat (about 400-450 degrees F.) Generously oil the grill--don't skip this step. (See Note 1) Halve the peaches and remove the pits. Lightly brush the sides and the skins with oil.Grill peaches until tender and lightly charred, but still firm enough to chop, about 4-5 minutes total, flipping halfway through.Chop the peaches into small, even pieces and add to a medium-sized bowl. Add in the diced red pepper, diced jalapeño, diced red onion, lime juice and coarsely chopped cilantro. Add in the chili powder, salt and pepper to taste (I add in 1/4 teaspoon of each, but add to your preference). Gently toss and taste. Adjust to personal preference (more salt/chili powder/lime juice). Refrigerate until ready to eat. Toss again right before adding to plates.
GLAZE: In a large bowl, combine the peach preserves, olive oil, soy sauce, mustard, garlic and jalapeño. Season to taste with salt and pepper (I add 1/4 teaspoon of each). Set aside 1/3 cup of this glaze for the end of the recipe.
CHICKEN: Halve the chicken breast(s) horizontally and pound the pieces to even thickness (don't want the chicken super-flat, just even so it will cook evenly). Drizzle each side with olive oil, salt, and pepper. Flip pieces and repeat -- oil, salt, pepper, seasoning. Place the prepared chicken on the grill. Grill for 8-10 minutes, flipping once in between halfway, and brushing generously with the peach glaze (not the 1/3 cup that you set aside), or until chicken juices run clear and internal temperature is at 160 to 165 degrees F. (carryover heat will take the chicken to 165 degrees F). Tent chicken with foil and let stand for 5-10 minutes.
SERVE: Brush the remaining 1/3 cup of the peach glaze over the cooked chicken and top with peach salsa (taste again before adding on top of the chicken and add any additional salt/pepper). Enjoy while hot.
Notes
Note 1: To oil the grill, I drench a roll-up paper towel in vegetable oil and, holding it with tongs, rub it over the grill grates. For a grill pan, brush 1 tablespoon oil over the pan.