Cook chopped bacon in a large pot over medium heat until crisp, about 6–8 minutes, then transfer to paper towels, leaving 1 Tbsp fat in the pan.
Add butter; when melted, stir in diced onion and celery and cook until translucent, about 3–4 minutes.
Sprinkle flour over vegetables and stir constantly for 1 minute until lightly golden.
Whisk in seafood stock, scraping up browned bits, nestle in reserved corn cobs, and simmer until slightly thickened, about 15 minutes.
Remove cobs; stir in corn kernels and simmer until tender, about 5 minutes.
Finish
Reduce heat to low; stir in heavy cream and crab meat and warm gently for 2 minutes without boiling.
Season with cayenne, salt, and pepper; ladle into bowls and top with bacon bits and chives.
Notes
After cooking, let the chowder rest off the heat for 10 minutes to allow flavors to meld.For leftovers, stir in the cream after reheating to maintain a silky texture and avoid curdling.