Combine barbecue sauce, peach preserves, garlic, and hot sauce in a medium saucepan, and heat over medium heat for 5-10 minutes.  Remove saucepan from heat and set aside.

Preheat oven to 400 degrees.

Line a rimmed baking sheet with aluminum foil.  Drizzle olive oil on top of foil and place chicken thighs skin side down on the baking sheet. 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.  Brush the tops with more sauce and return to the oven for 7 minutes. Remove from oven, brush on more sauce, and return to the oven for another 7 minutes. Once more, remove from oven, brush on sauce, and turn up the temperature to 425 degrees.

Continue roasting for another 5 to 7 minutes, or until the sauce is starting to brown around the edges and the thighs are totally cooked through. (170 degrees on digital thermometer.)  Either let rest for 10 minutes or serve immediately.