Melt the butter in a large Dutch oven or soup pot over medium-high heat.
Add the diced onion, carrots, and celery. Sauté for 5-7 minutes until the vegetables begin to soften.
Stir in the minced garlic, dried thyme, and oregano; cook for 1 minute until fragrant.
Sprinkle the flour over the vegetables and stir constantly for 1-2 minutes to cook off the raw flour taste.
Gradually pour in the chicken broth while whisking continuously to prevent lumps from forming.
Add the raw chicken breasts directly into the pot. Bring the mixture to a boil, then reduce heat to low, cover, and simmer for 15-20 minutes, or until the chicken is cooked through.
Remove the chicken breasts to a cutting board. Shred the meat with two forks or chop into bite-sized cubes.
Return the chicken to the pot. Stir in the heavy cream and let the soup simmer uncovered for another 5 minutes to thicken slightly.
Season with salt and black pepper to taste. Serve warm with crusty bread.