In large saucepan, combine squash and broth. Bring to boil, then reduce heat to medium. Simmer until squash is very tender, about 20 minutes.
Remove from heat and let stand until slightly cooled; puree in batches in blender.
Return puree to saucepan and place over medium-low heat. Stir in sour cream, cheddar, butter and red pepper. Season with salt and pepper.
Stir until heated through (do not allow to boil). Taste soup, adding sugar if squash was not particularly sweet. Serve sprinkled with chives.
Recipe courtesy Chef Jon Ashton