Melt butter in a stockpot over medium-low heat. Add in carrots, jalapeño, and onion, and allow to cook until vegetables are tender, about 3-4 minutes. Stir flour into the vegetables.
Slowly mix in the milk, broth, cream-style corn, roasted corn, chicken, pepper, and salt. Bring heat up to medium-high heat. Bring to a boil, then lower the heat to medium and allow to cook 10 minutes.
Meanwhile, cook bacon in a skillet. Once cooked, transfer the bacon slices to a paper towel lined plate. Allow to cool, and then crumble the bacon. Add the bacon to the soup mixture. Top soup with the optional fresh chives.