Melt butter in a large pot and cook onion, celery, and bell pepper for 5 to 6 minutes until softened.
Sprinkle in flour and stir constantly for 1 to 2 minutes to form a roux.
Gradually whisk in the stock until smooth.
Add the corn cobs and potatoes. Simmer 15 to 20 minutes until potatoes are tender.
Remove and discard the corn cobs. Stir in corn kernels and simmer 5 more minutes.
Reduce heat to low and stir in the cream, warming gently without boiling.
Fold in the crab meat and warm through for 2 to 3 minutes. Season with salt and pepper.
Ladle into bowls, top with chives, and serve with hot sauce if desired.