Cook the bacon in a large pot over medium heat until crisp. Move it to a paper towel and pour off all but about two tablespoons of the 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.
Scoop out roughly two cups of the soup, blend it smooth, and stir it back in. This thickens the chowder without any flour.
Add the corn and half-and-half and warm through for 5 minutes. Season, then top each bowl with the bacon and chives.