In a large saucepan or soup pot (I used my Dutch ovem), cook the bacon for 3-4 minutes over medium-high heat, until it starts to crisp. Remove the bacon with a slotted spoon and set aside.
Add the celery, carrots and onion to the pot with the bacon grease and saute until crisp-tender, about 5 minutes.
Add garlic, salt, parsley, thyme, and red pepper flakes and cook 1 minute, then add the chicken broth and bring to a boil.
Combine chicken broth with the chicken breasts (uncooked) and rice. Cover, reduce heat to medium-low and cook for 12-14 minutes, until chicken is cooked through (it will reach an internal temperature of 165 degrees F) and rice is al dente.
Remove the chicken to a cutting board and shred it.
Whisk together milk and corn starch to make a cornstarch slurry and stir it into the pot with the shredded chicken. Cook for 2-3 minutes, until thickened, and stir the bacon back in before serving.
