Prepare the Corn Stock: In a large stockpot, combine the stripped corn cobs, chicken broth, milk, and heavy cream over medium-high heat. Bring the mixture to a boil, then lower the heat and simmer uncovered for about 20 minutes. Remove from heat and discard the cobs. Set the stock aside.
Cook the Bacon: Heat a large Dutch oven or heavy-bottomed pot over medium-high heat. Add the chopped bacon and cook, stirring occasionally, until it is browned and crispy, about 5 to 7 minutes. Remove the bacon with a slotted spoon and place it on a paper towel-lined plate. Keep the rendered fat in the pot.
Sauté the Vegetables: Add the diced celery, onion, and carrot to the pot with the bacon fat. Cook over medium-high heat, stirring occasionally, for about 7 to 8 minutes, or until the onion softens and becomes translucent.
Build the Chowder: Stir in the reserved corn kernels, diced potatoes, salt, black pepper, and cayenne pepper. Pour in the prepared corn stock, then bring the mixture to a gentle boil. Reduce the heat to low and let the chowder simmer uncovered for 10 to 15 minutes, stirring occasionally, until the potatoes are fork-tender. Taste and adjust the seasoning if needed.
Serve: Ladle the chowder into bowls and top each serving with the reserved crispy bacon and a sprinkle of fresh chives for garnish.
Storage: Transfer any leftovers to an airtight container and store in the refrigerator for up to 4 days.