Preheat the oven to 350°F. Grease a 9-by-9-inch baking dish. In a medium bowl, beat the eggs and the half and half. Add the salt, black pepper, cayenne pepper, chives, corn and half of the cheese. Place the butter in a microwave-safe container and heat for approximately 1 minute on high to melt. Add the cracker crumbs to the butter and mix. Add half of the cracker crumbs to the corn mixture and mix well. Transfer the corn to the prepared baking dish.