Cook bacon in a large pot over medium heat until crisp. Drain on a paper towel; pour off all but about two tablespoons fat.
Cook the onion and celery in the reserved fat until soft, 5 to 6 minutes. Add the garlic and cook 30 seconds.
Add the potatoes, broth, and smoked paprika. Simmer until the potatoes are tender, about 15 minutes.
Blend roughly two cups of soup smooth; stir back in to thicken without flour.
Add the corn and half-and-half and warm through for 5 minutes. Season, then top each bowl with the bacon and chives.