Preheat oven to 425F.
In a medium bowl, toss carrots with 1 tablespoon of olive oil and season with salt and pepper. Season chicken thighs with salt and pepper. Prep the rest of your ingredients.
In a cast-iron pan or other oven-safe skillet, heat 1 tablespoon of olive oil over medium-high heat. Add chicken thighs and sear 2 minutes per side. Remove chicken and transfer to a plate. Do not discard pan drippings.
Add vinegar to pan and scrape up bottom bits from pan with a wooden spoon. Add garlic, maple syrup, mustard, thyme, and lemon juice. Bring to a simmer.
Return chicken to skillet and spoon sauce over thighs.
Nestle carrots into skillet. Bake until chicken is cooked through and carrots are tender, 20 minutes. Serve with sauce.