Combine barbecue sauce, peach preserves, garlic, and hot sauce in a saucepan and heat over medium heat for 5-10 minutes or until nice and hot. Set aside.
Preheat oven to 400 degrees Fahrenheit.
Drizzle olive oil on two rimmed baking sheets and place chicken thighs skin side down in the pans.
Roast for 25 minutes.
Remove from oven briefly, brush sauce all over the thighs, then use a spatula to flip them over to the other side, being careful not to ear the skin. Brush the tops with more sauce and return to the oven for 7 minutes.
Remove from oven, brush on more sauce, and return the oven for another 7 minutes.
Remove from oven, brush on sauce, and turn up the temperature to 425 degrees Fahrenheit.
Continue roasting for another 5 to 7 minutes, or until the sauce is staring to brown around the edges and the thighs are totally cooked through.
Remove from the oven and let sit for at least 10 minutes before serving.