How to Make It
Preheat oven to 400°F. Reserve 1 teaspoon Italian dressing mix. Toss together carrots, potatoes, oil, and remaining dressing mix on an aluminum foil-lined rimmed baking sheet, and arrange in a single layer.
Arrange chicken on top of carrot and potato mixture; sprinkle chicken with reserved dressing mix.
Bake in preheated oven until chicken is golden brown and a thermometer inserted in thickest portion registers 165°F, 35 to 40 minutes. Transfer chicken to a platter.
Add green beans to potato and carrot mixture; toss to coat. Add chicken back to baking sheet on veggies. Bake at 400°F until beans are crisp-tender, about 7 minutes. Toss veggies with butter, if desired, and serve with chicken.