Place bacon pieces in a large Dutch Oven or soup pot over medium heat and cook until bacon is crisp and browned.
Remove bacon pieces and set aside, leaving the fat in the bottom of the pot.
Add butter and chopped onion and cook over medium heat until onions are tender (3-5 minutes).
Add garlic and cook until fragrant (about 30 seconds).
Add diced potatoes to the pot along with chicken broth; stir well.
Bring to a boil and cook until potatoes are tender when pierced with a fork (about 10 minutes).
Add half and half, heavy cream, salt, and pepper; stir well
Reduce heat to simmer.
Using a stick blender (also called an immersion blender), puree about half of the soup.
Stir in 1 cup sour cream and half of the reserved bacon pieces, stir well.
Allow soup to simmer for 15 minutes before serving.
Top each bowl with additional sour cream, bacon, cheddar cheese, and chives.