Cut acorn squash in half and bake until tender, about 40 - 45 minutes. Remove from the oven.
Meanwhile, discard dark green part of the leek. Leeks usually tend to be sandy, so I like to clean them well by separating the layers and washing them well under cold water. Chop leeks and sauté in a large pot with butter or oil over medium low heat until tender, about 5 minutes.
When squash is cool enough to handle, scoop out seeds and discard. Scoop out the flesh from the skin and add to the pot with leeks.
Add about 2/3 of the chicken stock to the pot; stir well and simmer about 5 minutes. Using an immersion blender or a regular blender, blend soup until smooth. Add remaining broth and simmer a few more minutes. Adjust salt and pepper to taste. Garnish with pepitas and chopped chives.