Preheat a grill or grill pan to medium-high heat (400–450°F / 205–230°C). Lightly oil the grill grates.
Halve the peaches, remove the pits, and brush lightly with olive oil.
Grill the peaches for 4–5 minutes, turning once, until lightly charred but still firm.
Dice the grilled peaches and place them in a mixing bowl.
Add the red bell pepper, jalapeño, red onion, lime juice, cilantro, chili powder, salt, and pepper. Toss gently and refrigerate until ready to serve.
In another bowl, whisk together the peach preserves, olive oil, soy sauce, Dijon mustard, garlic, and jalapeño. Reserve ⅓ cup of the glaze for finishing.
Slice the chicken breasts horizontally into thinner cutlets and pound gently to an even thickness.
Brush both sides with olive oil and season with salt and pepper.
Grill the chicken for 8–10 minutes, turning once halfway through. Brush generously with the glaze (excluding the reserved portion) while grilling.
Cook until the internal temperature reaches 165°F (74°C).
Let the chicken rest for 5–10 minutes under loose foil.
Brush the reserved glaze over the cooked Peach Salsa Chicken and generously spoon the fresh peach salsa on top before serving.