Preheat your grill for indirect or two-zone grilling (where one side has heat and one side doesn't) to 375 or 400 degrees F.
Cut the ends off of the spaghetti squash and then cut in half lengthwise. Scrape out the seeds and pulp with a large spoon. Place each half of the squash cut side up on a metal baking sheet. Drizzle each half of the squash with the olive oil and season with salt and pepper.
Place the baking sheet on the side of your grill with no direct heat and close the lid. Roast for 45-60 minutes (depending on how big your squash is. Check the squash with a fork for tenderness, the strands should pull apart easily when it is done.