Preheat oven to 450F.
In a 9x13 oven-safe casserole dish toss potatoes and carrots with 1 tbsp olive oil and ¼ tsp salt. Place chicken quarters on top--it's ok if they are touching.
In a small bowl, whisk all ingredients together for the marinade. Pour overtop of chicken and vegetables.
Roast in the oven for 45-50 minutes, or until chicken reaches 165F when checked with an instant read thermometer. Check chicken after 30 minutes, if it is browning too much, cover with aluminum foil.