Prepare a hot grill fire or a grill pan over medium heat. Brush peach halves and onion rings with 1 tablespoon oil. Grill until onions and peaches are charred and onions are softened. Cool slightly, then slice peaches and separate onion rings.
In a small jar with a tight-fitting lid, combine lemon juice, 2 tablespoons oil, mustard, salt, and pepper. Shake vigorously to combine.
In a large bowl, toss spinach with dressing and divide between plates. Top with peaches, onions, and chick’n.