Combine onion, celery, butter, and garlic in a saucepan. Cook over medium heat until onion softens, about 4 minutes.
Add flour and thyme. Cook 1 minute more. Stir in corn and potatoes.
Add broth, cream, salt, and pepper. Simmer 15-20 minutes uncovered or until potatoes are tender.
Garnish with chives and serve warm.
