Preheat oven to 425 degrees F. Line a large baking sheet with parchment paper or foil (for easy clean-up)
Lay chicken breasts onto prepared baking sheet. Whisk together brown sugar and Italian dressing mix in a small bowl. Set aside.
Rinse and dry zucchini and red potatoes. Slice and cube both into small bite-size pieces. Lay the vegetables out onto tray next to chicken.
Sprinkle 1/4 cup brown sugar mixture over each chicken breasts, lightly patting onto breast. Then sprinkle remaining mixture onto the vegetables. Season everything with a little salt and pepper. Place pan in preheated oven and bake for 30 minutes or until chicken is cooked through and no longer pink in center.
Turn broiler on high and broil chicken another 1 to 2 minutes or until brown sugar caramelizes. (Stay and watch closely so it doesn't burn! Very important.)
Serve immediately and enjoy!