Preheat the oven to 375°F (190°C).
Prepare the bell peppers by slicing the tops off and removing the seeds. If needed, trim the bottoms slightly for stable standing. Place them upright in a baking dish.
In a mixing bowl, combine the shredded chicken, basil pesto, half of the mozzarella cheese, cherry tomatoes, and season with salt and pepper. Mix until all the ingredients are well incorporated.
Spoon the chicken mixture evenly into each prepared bell pepper.
Top each stuffed pepper with the remaining mozzarella cheese and a sprinkle of grated Parmesan cheese.
Drizzle a little olive oil over the top of the stuffed peppers.
Cover the baking dish with foil and bake in the preheated oven for 20 minutes.
After 20 minutes, remove the foil and bake for an additional 10 minutes, or until the peppers are tender and the cheese is bubbly and golden.
Remove from the oven and let cool for a few minutes before serving.