Preheat oven to 400 degrees.
Season chicken generously on both sides with salt and pepper. Heat ½ tablespoon of oil in a large oven-proof skillet over medium-high. Add chicken, skin side down, and cook until browned, 5 minutes. Transfer skillet to oven. Roast until skin is crispy and chicken is cooked through, 15 to 20 minutes.
Meanwhile, mix shallots or onion, lemon juice, honey, and ¼ teaspoon sea salt in a small bowl. Let stand 10 minutes; stir in peaches.
In a small sauté pan, heat a drizzle of olive oil on medium-high heat. Add snap peas and cook, stirring occasionally, until lightly charred and crisp-tender, 3 minutes.
Check the chicken to make sure juices run clear, then remove from oven. Serve chicken with blistered snap peas and peach salsa.