If you use chicken breasts that weigh more than 8 ounces, your cooking times will be different and you run the risk of overreducing the apple cider. You can substitute apple juice if apple cider is unavailable, though the resulting sauce will be less rich.
Pat chicken dry with paper towels and sprinkle with ½ teaspoon salt and ¼ teaspoon pepper. Spread flour in shallow dish.
Melt butter in 12-inch nonstick skillet over medium-high heat. Dredge chicken in flour to coat, shake to remove excess, and add to skillet. Place apple cut side down in skillet around chicken. Cook, flipping apple as needed, until evenly browned on cut sides and chicken is golden brown on bottom, about 5 minutes.
Flip chicken. Leaving chicken and apple in skillet, add onion, remaining ¼ teaspoon salt, and remaining ¼ teaspoon pepper and cook, stirring occasionally, until onion is softened and browned, about 4 minutes.
Add cider and thyme sprigs to skillet and bring to boil. Reduce heat to medium-low, cover, and simmer until chicken registers 160 degrees, 6 to 8 minutes.
Transfer chicken to platter. Add cream to skillet, increase heat to medium-high, and bring to boil. Cook until sauce has thickened slightly, about 2 minutes. Stir in vinegar and any accumulated chicken juices. Discard thyme sprigs and season with salt and pepper to taste. Spoon sauce and apple over chicken and sprinkle with chives. Serve.
Don't Worry About a Full Skillet
