How to Make It
Preheat oven to 425˚F. Cut squash in half lengthwise; discard seeds. Coat squash evenly with 2 tablespoons of the oil. Place cut side down on a rimmed baking sheet. Bake in preheated oven until tender, about 45 minutes. Remove squash from oven, and flip over. Let stand 15 minutes to cool. Gently scrape interior of squash from edges, and place in a large bowl. Separate into strands with forks. Sprinkle with 1 teaspoon of the salt and 1/2 teaspoon of the pepper.
Heat cream cheese and remaining 2 tablespoons oil in a large skillet over medium. Cook, stirring occasionally, until cheese is melted, about 2 minutes. Stir in chicken, and cook, stirring occasionally, until coated and warmed through, about 3 minutes. Stir in Parmesan, 2 ounces of the mozzarella, and 1 cup of the marinara. Cook, stirring occasionally, 2 minutes. Add marinara mixture to squash strands, gently toss to swirl together, but do not over mix.
Place squash shell halves, cut side up, in a 13- x 9-inch baking dish. Divide mixture among squash shells; spread remaining 1/2 cup marinara evenly on tops of stuffed squash halves, and sprinkle with remaining 6 ounces mozzarella. Bake at 425°F until cheese is melted and lightly browned, about 15 minutes. Remove from oven, and sprinkle with basil and remaining 1/2 teaspoon each of salt and pepper.