Preheat the broiler. Pat the catfish dry, rub with olive oil, and season with paprika, salt, and pepper. Broil 6 inches from the heat for 6 to 8 minutes until browned. Flake into bite-sized pieces.
In a large pot, cook the bacon until crisp. Remove and set aside, leaving the fat in the pot.
Add the onion and celery and cook 5 minutes. Add the garlic and cook 30 seconds more.
Sprinkle the flour over the vegetables and stir constantly for 2 minutes.
Gradually whisk in the stock. Add the potatoes and bring to a simmer.
Cook 15 to 18 minutes, until the potatoes are fork-tender.
Stir in the heavy cream and Swiss chard, and simmer 3 to 4 minutes until wilted.
Fold in the flaked catfish, season, and warm through 2 minutes. Top with the reserved bacon.