Pat chicken pieces dry with a paper towel, and coat all sides with olive oil. Combine chili powder, garlic powder, sugar, salt, and white pepper in a small bowl; mix well. Rub spice mixture on chicken pieces, see note.
Preheat an outdoor grill to medium-high, and clean the grates.
Meanwhile, stir peach preserves, hoisin sauce, grated ginger, garlic powder, Sriracha, and lime zest together in a small saucepan over medium heat. Heat, stirring, until the preserves are melted and ingredients are well blended, about 3 to 5 minutes. (You will use half of peach glaze during the last minutes of cooking chicken, and reserve half until ready to serve).
When the grill is ready, saturate a paper towel with cooking oil, and use tongs to oil the grates.
Grill chicken about 4 to 5 minutes per side, depending on thickness, until the internal temperature reads about 155 degrees F (68 degrees C) with an instant read thermometer. Brush chicken with peach glaze and grill 1 minute more, then turn the chicken and brush glaze on the other side. Continue grilling and turning until the chicken reaches 160 degrees F (71 degrees C). Remove to a plate and cover with foil. During rest, residual heat will raise the internal temperature to 165 degrees F (74 degrees C).
Meanwhile, grill peaches. Using tongs, place peach halves on the hot grates, cut side down, and grill just until there are grill marks, 1 to 2 minutes.
To serve, place chicken and peach halves on a serving plate and brush with reserved glaze. Squeeze half a lime over the entire dish. Garnish with additional lime slices, if desired.
