In a large heavy-bottomed Dutch oven over medium heat, cook the diced bacon until the fat has rendered and the pieces are crispy.
Using a slotted spoon, remove the bacon to a paper-towel-lined plate, reserving 3 tablespoons of bacon fat in the pot.
Add the onion, celery, red bell pepper, and minced jalapeños to the pot. Sauté for 6-8 minutes until the vegetables are softened and the onions are translucent.
Stir in the minced garlic and cook for 60 seconds until fragrant.
Sprinkle the flour over the vegetables and stir constantly for 2 minutes to cook out the raw flour taste, creating a light blonde roux.
Slowly whisk in the chicken broth, one cup at a time, ensuring no lumps form. Increase heat to medium-high and bring to a gentle simmer.
Reduce heat to low. Whisk in the heavy cream and cubed cream cheese. Stir continuously until the cream cheese is fully melted and the soup is smooth.
Gradually add the shredded cheddar cheese, whisking in small handfuls until completely incorporated.
Fold in the shredded chicken and half of the crispy bacon. Season with smoked paprika, salt, and black pepper.
Simmer on low for an additional 5 minutes to allow flavors to meld. Do not let the soup reach a rolling boil after the cheese is added to prevent curdling.
Serve immediately, garnished with the remaining crispy bacon, reserved jalapeño slices, and fresh chives.