Season both sides of the chicken pieces with salt and pepper. Place the flour in a shallow bowl, and dredge the chicken pieces in the flour, shaking off the excess. In a large skillet, heat the olive oil over medium-high heat. Add the chicken pieces to the pan and saute until lightly golden, about 2-3 minutes per side, and an instant-read thermometer reads 160˚ F in the thickest part of the chicken. (Keep in mind that pieces of different sizes will finish cooking at different times to avoid overcooking.) Remove the chicken pieces to a plate, tent with foil, and set aside.
Add the garlic and thyme leaves to the pan and sauté just until fragrant, about 1 minute. (If necessary, add an additional small drizzle of olive oil if most of the oil was absorbed by the chicken.) Off the heat, add the wine to the pan, scraping the bottom of the pan to loosen any browned bits. Return the pan to the heat and bring the liquid to a simmer. Stir in the chicken broth. Reduce until the sauce has thickened, about 4-5 minutes. Add the lemon juice to the pan. Add in the butter and whisk until completely melted. Season with salt and pepper to taste. Serve immediately, spooning the sauce over the chicken.