Start by prepping your vegetables: thinly slice the carrots, dice the celery and onion, and mince the garlic. Set everything aside on your cutting board.
Place the chicken breasts in the bottom of your slow cooker. Pour in the chicken broth, making sure it just covers the chicken. Sprinkle the dried thyme evenly over the top, then season with a pinch of salt and pepper.
Add the sliced carrots, diced celery, diced onion, and minced garlic over the chicken. Spread the veggies out evenly so they can soften and release their flavors as they cook.
Cover the slow cooker with its lid and set it to low. Let everything simmer gently for 6 to 8 hours. During this time, the house will fill with a warm, herbal aroma, and the chicken will become impossibly tender.
Once the cooking time is up, open the lid and check that the chicken is cooked through and shreds easily with two forks. Remove the chicken breasts and shred them into bite-sized pieces.
Return the shredded chicken to the slow cooker and stir everything together. Taste the broth and adjust the seasoning with more salt, pepper, or herbs as needed. Let it sit uncovered for about 10 minutes to allow the flavors to meld.
Serve the soup hot, garnished with freshly chopped parsley. Pair it with crusty bread or your favorite side for a cozy, nourishing meal.