Remove corn from the cob and set it aside for the chowder. Remove as much skin as possible from the cobs, then place in a pot.
Add chicken broth, milk, and cream. Bring to a boil, then reduce heat and simmer uncovered for about 20 minutes while preparing chowder.
Place a Dutch oven over medium-high heat. Cook bacon, occasionally stirring, until crisp. Remove with a spoon and set aside.
In the same pan, cook onion, celery, and carrot in bacon fat uncovered, occasionally stirring, until onion is softened, about 7 to 8 minutes.
Using tongs, remove cobs from the broth. Add potatoes, corn, salt and pepper, and cayenne pepper to the Dutch oven.
Pour the broth into the pot and bring to a boil, then simmer uncovered for 10 to 15 minutes or until the potatoes are tender. Adjust seasoning to taste. To taste, pour into bowls and garnish with reserved bacon and chopped chives.