Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish with olive oil.
In a large mixing bowl, combine the shredded chicken, sliced zucchinis, cherry tomatoes, garlic powder, Italian seasoning, salt, and black pepper. Mix until well combined.
In a separate bowl, mix the cream cheese, half of the mozzarella cheese, and half of the Parmesan cheese until smooth.
Add the cheese mixture to the chicken and zucchini mixture, stirring until everything is evenly coated.
Pour the mixture into the prepared baking dish, spreading it out evenly. Top with the remaining mozzarella and Parmesan cheeses.
Bake in the preheated oven for 25-30 minutes, or until the cheese is bubbly and golden brown.
Remove from the oven and let it cool for 5 minutes. Garnish with fresh basil if desired before serving.