Preheat the oven to 400°F (200°C). Cut the spaghetti squash in half lengthwise and scoop out the seeds. Drizzle with olive oil, season with salt and pepper, and place cut-side down on a baking sheet. Bake for 30-40 minutes until tender.
While the squash is baking, sauté the spinach and garlic in a skillet over medium heat until wilted.
Mix the cooked chicken, spinach, ricotta cheese, and half of the mozzarella cheese in a bowl. Season with salt and pepper.
Once the squash is done, use a fork to scrape the strands of squash into "spaghetti." Mix the squash strands with the chicken and cheese mixture, then stuff the mixture back into the squash shells.
Top with the remaining mozzarella and Parmesan cheese. Return to the oven and bake for 10-15 minutes, or until the cheese is melted and bubbly.