While pasta cooks, cut bell peppers into long, thin strips and then halve the slices. Chop chives. Make dressing and set aside.
Keep water in pot and remove cooked pasta from the pot and set aside.
Toss carrots and bell pepper into the water. Set to medium heat and cook for five minutes, or until veggies reach desired firmness. Remove carrots and bell peppers from the pot.
Toss pasta, chicken and veggies with dressing and top with chives, red pepper flakes (if desired) and fresh tarragon.