Cook the chopped bacon in a skillet over medium heat until crisp. Remove the bacon with a slotted spoon and set it aside, leaving 1 tablespoon of the drippings in the pan.
Add the sliced leeks and minced garlic to the skillet. Cook for 3 minutes until the leeks soften slightly.
Place the cubed potatoes, chicken broth, dried thyme, cooked leeks, garlic, and most of the bacon into the slow cooker. Stir to combine.
Cover and cook on low for 6 hours or until the potatoes are very tender.
Stir in the heavy cream, then season with salt and black pepper. Let the soup sit for 5 minutes to warm through.
Ladle into bowls and top with the remaining bacon pieces and chopped chives.