Position a rack in the upper third of the oven and preheat to 450 degrees.
Pat the chicken dry and season with salt and pepper. Dust the skin side with flour. Place a large ovenproof skillet over medium-high heat, add the olive oil and heat until shimmering. Add the chicken, skin-side down, and cook until the skin is golden, about 5 minutes. Turn the pieces and pour off the excess fat. Tuck the shallots under and around the chicken and cook until just golden, about 2 more minutes.
Push the chicken aside, then stir in the tomato paste and thyme and cook until the paste darkens, about 30 seconds. Add the vinegar, apple cider and raisins, bring to a boil and simmer 1 minute. Transfer the skillet to the oven and roast the chicken until just cooked through, 10 to 12 minutes.
Transfer the chicken, skin-side up, to a heatproof serving dish and return to the oven (turn the oven off). Bring the sauce left in the pan to a boil and reduce by half, 3 to 4 minutes. Lower the heat and whisk in the butter. Spoon the sauce over the chicken.
Photograph by Antonis Achilleos
Courtesy of Food Network Magazine