In a large pot, saute bacon over medium heat until browned and crispy, about 5 minutes. Remove with a slotted spoon to a plate lined with paper towels. Set aside.
Add butter to the pot and heat until melted. Add onions and thyme; saute until softened, about 6 minutes. Add potatoes and stock. If necessary, add enough water to barely cover. Bring to a boil. Reduce heat and simmer until potatoes are almost tender, about 15 minutes. Add fish, salt and pepper; simmer until fish is opaque and flakes easily with a fork and potatoes are tender, about 5 minutes.
Using a slotted spoon, gently transfer fish to a large plate. Using a fork, flake fish apart and set aside.
Stir cream into the pot and reheat over medium heat until steaming, stirring often. Do not let boil. Taste and adjust seasoning with salt and pepper, if necessary. Return fish to the pot.
Ladle into heated bowls and garnish with reserved bacon and chives.
Tip: If you don't have fish stock on hand, you can replace it with 4 cups chicken stock and 1 cup clam juice.