Preheat oven to 425°F. Set an oven rack to the middle position.
Rinse chicken pieces and pat dry. Wash potatoes and carrots and pat dry.
Zest lemon, cut in half and juice the whole lemon.
Finely chop rosemary, thyme, and garlic with a knife or in a mini food processor. Mix together with lemon juice, lemon zest, 4 tablespoons olive oil, salt, and pepper.
In a large bowl, or directly on the sheet pan, toss potatoes and carrots with half of the lemon marinade and spread out over the pan.
Toss the chicken pieces with the remainder of the lemon marinade and arrange on the sheet pan. Be sure everything is in a single layer.
Drizzle the remaining 1 tablespoon olive oil, if needed, over the chicken, potatoes, and carrots.
Place into the oven and bake for 35-40 minutes, depending on the size of your chicken pieces. Check to make sure the potatoes are cooked through by piercing with a fork.
Remove from the oven and let rest for 5-minutes before serving.