For glaze: In a bowl, combine peach preserves, oil, soy sauce, mustard, garlic, and jalapeño. Season with salt and pepper. Reserve ½ cup of glaze.
For chicken: Brush chicken with oil and season with salt and pepper. Place skin-side down on the grill and cook for 6 to 7 minutes, or until golden brown. Turn over chicken and continue cooking for 5 to 6 minutes. Brush both sides with glaze and continue cooking for an additional 4 to 5 minutes.
Place peach halves, cut side down on the grill and cook for 2 minutes. Turn over and brush with reserved glaze. Cook for 3 to 4 more minutes, or until peaches are soft.
Serve chicken with grilled peaches on the side.