Preheat oven to 180°C.
Season the chicken with salt.
Heat the oil in a large casserole dish over medium-high heat. Add the chicken pieces and cook on each side until the flesh changes colour. Transfer them to a plate.
Add the vinegar to the pan and scrape up bottom bits with a wooden spoon. Add the minced garlic, maple syrup, mustard, thyme and lemon juice, then simmer to thicken. When the sauce is glossy, return chicken and the pan juices, add the carrot bits and spoon the sauce over ever them, coating everything well.
Season with salt and pepper and bake in the oven until the chicken golden and cooked through, while the carrots are tender. This should take about 30-35 minutes.
Serve the chicken and carrot with the pan sauce.