Bring a pot of salted water to a boil and cook the chicken breasts for 10-15 minutes. Drain, shred, and set aside.
Heat a dry pan and crisp the bacon for a minute. Transfer to a plate lined with paper towels and set aside.
Heat the butter in a saucepan and sauté the garlic for 30 seconds over medium heat until fragrant. Add the broth and heavy cream, turn the heat to high and allow to simmer for a minute.
Add the cream cheese and stir to melt into the soup.
Add half the shredded chicken, simmer for 10 minutes, and season to taste with salt and pepper.
Using an immersion blender, process the soup until creamy and thick.
Add the remaining chicken and cook for 5 more minutes.
Serve hot, topped with crispy bacon bits, drizzled with olive oil, and garnished with fresh dill.