Preheat oven to 400°F.  Line a baking sheet with parchment paper.  

Using a sharp knife, cut the top off of the squash then microwave for 3-4 minutes to slightly soften the squash.  Cut in half lengthwise.  

Scoop the seeds out of the inside.  Sprinkle with salt & pepper and drizzle with olive oil.  Place face down on the lined baking sheet.  Bake for 40-45 minutes.  

While the squash is baking mix 1 cup of the cheese, half & half, thyme, garlic, salt and pepper in a large mixing bowl.  

When the squash is done baking, let it cool for about 15 minutes.  Then using fork scrape the squash lengthwise to form the spaghetti strands.  Add the squash to the cheese mixture and mix well until everything is combined. 

Scoop the mixture back into the squash.  Depending on the size of the squash and your preference, you may be able to get all of it into one half of the squash.  Return the squash to the baking sheet and sprinkle with the remaining ¼ cup of cheese.  Bake for an additional 15 minutes.  Top with chives and serve immediately.