Cook diced potatoes in small amount of boiling salted water for 10 minutes until tender; drain and set aside.
In a large skillet cook bacon until crisp; remove to paper towels. DO NOT DRAIN GREASE.
Saute chopped onion in the bacon grease over low heat until translucent; then add the minced garlic, stirring, until you have smelled the garlic for 30 seconds. Remove from heat.
In a medium-sized saucepan melt the butter over low-medium heat and stir in the flour until it forms a paste. Slowly add the chicken broth and half and half, stirring constantly until it begins to thicken. If it gets too thick, add a little more broth.
When mixture reaches desired consistency, add the potatoes, onion-garlic mixture, crumbled bacon (all but two slices), salt and pepper to taste, and the cheese slices. Stir until cheese is melted and fully incorporated into the soup.
Ladle into individual soup bowls, top with remaining crumbled bacon and chives.