Melt butter in a large pot over medium heat. Add onion and cook until softened, about 5 minutes.

Add potatoes and chicken broth to the pot. Bring to a boil, then reduce heat and simmer until potatoes are tender, about 15-20 minutes.

Using an immersion blender or regular blender (in batches), blend the soup until smooth and creamy.

Stir in heavy cream, salt, and pepper. Heat through, but do not boil.

Serve hot, garnished with chopped chives.