Using a meat tenderizer, flatten the meat a bit and sprinkle with salt and pepper:
Heat oil in a skillet over medium-high heat. Add carrots and 1/2 the balsamic/honey mixture to the skillet and cook for about 5 minutes, until beginning to become tender.
Fill each tenderloin with a spoonful of the cooked carrots and a slice of avocado:
Roll up and place a toothpick horizontally through the chicken to hold it together:
Drizzle with remaining balsamic/honey mixture and cook in skillet (add a bit more oil if necessary) over medium heat, about 3-4 minutes per side: