Combine the barbecue sauce, peach preserves, garlic and hot sauce to taste in a medium saucepan and heat over medium heat until nice and hot, 8 to 10 minutes. Set aside.
Preheat the oven to 400 degrees F.
Drizzle some olive oil on 2 rimmed baking sheets and place the chicken thighs skin-side down. Roast for 25 minutes. Remove from the oven, brush some sauce all over the thighs, then use a spatula to flip them over, being careful not to tear the skin. Brush the tops with more sauce and return to the oven for 7 minutes more. Remove from the oven, brush on more sauce, and return to the oven for another 7 minutes. Remove from the oven, brush on more sauce, and increase the oven temperature to 425 degrees F.
Continue roasting the chicken thighs until the sauce is starting to brown around the edges and the thighs are totally cooked through, 5 to 7 minutes more. Remove from the oven and let sit for at least 10 minutes before serving. Delicious!