Combine marinade for chicken and split into two portions. Place each chicken half into a resealable plastic bag. Pour half of marinade into each bag, making sure chicken is completely covered. Seal bags and place into refrigerator for 1 hour.
Preheat grill for medium heat. Remove chicken from bag and place onto grill. Cook for 45 minutes turning occasionally. Chicken will be done once it reaches between 175-180 degrees F. in thigh and at least 165 degrees F. in breast meat.
For potatoes: Place fingerling potatoes and cut onion onto the center of aluminum foil sheet. coat with olive oil, salt, black pepper and thyme. Gather ends of foil and begin rolling downward. Do not make packet too taut, Leave a few inches to allow movement of steam. Seal all edges. Place onto grill right after chicken goes on grill
For carrots: Trim greenery, wash, and pat dry. Place onto center of aluminum foil. Combine lemon juice, oil, and brown sugar in a small bowl. Pour over top. Repeat same closure process as potatoes. Put onto grill 15 minutes after chicken is placed on grill.
For corn: combine olive oil and minced garlic in small bowl. Brush corn with mixture and place onto grill during the last 5-7 minutes of cooking time. It will cook quickly, so turn often.
Once everything is cooked. Remove chicken (carve chicken or keep as is) and place onto center of large platter. Carefully open foil packets and check for doneness and arrange around the chicken. Cut corn into thirds and place onto platter. Garnish with fresh thyme and a squeeze of lemon over top.