Preheat the oven to 375°F and lightly grease a 9x9 inch baking dish.
Cook the penne in a large pot of boiling salted water until al dente, then drain and set aside.
Heat the olive oil in a skillet over medium heat. Add the minced garlic and cook for 1 minute until fragrant.
Stir in the cream cheese and heavy cream. Cook until the cream cheese melts and the mixture is smooth.
Add the shredded chicken, drained spinach, chopped artichoke hearts, salt, and pepper. Stir until everything is evenly coated.
Combine the sauce mixture with the cooked pasta in a large bowl.
Transfer the mixture to the prepared baking dish. Sprinkle the mozzarella and Parmesan evenly over the top.
Bake for 20 to 25 minutes until the cheese is melted and lightly browned on top.