Cook the wild rice according to package directions. Drain off any excess cooking liquid and set aside.
Preheat your oven to 350 degrees F. Lightly coat a 9×13-inch baking dish with cooking spray and set aside.
In a large, deep skillet, heat 2 tablespoons of olive oil over medium heat. Add the diced chicken and sauté until the chicken is cooked through and no longer pink on the inside, about 6 minutes. Remove to a paper towel-lined plate and set aside.
With a paper towel, carefully wipe the skillet clean. Heat the remaining 2 tablespoons of olive oil over medium. Add the diced butternut squash, onion, salt, and pepper. Sauté until the onion begins to soften, about 2 minutes.
Cover and cook, stirring occasionally, until the squash is tender but still retains some chew, about 6 to 8 minutes. Stir in the thyme, cranberries, reserved chicken, rice, and 1/4 cup of Parmesan cheese. Mix well to combine all those delightful flavors.
Transfer the mixture to the prepared baking dish, spreading it evenly. Bake in the oven for 20 minutes, then remove from the oven and sprinkle with the remaining 1/4 cup of Parmesan cheese. Bake for an additional 5 minutes, until the cheese melts.
Sprinkle with additional chopped fresh thyme before serving warm.
