Place the chicken breasts at the bottom of your slow cooker, then add diced carrots, celery, and chopped onions over the chicken. Pour in chicken broth until the ingredients are mostly covered, then sprinkle with thyme or parsley and season with salt and pepper.
Cover with the lid and cook on low for about 6 hours, until the chicken is tender and easily shredded, and the vegetables are soft and fragrant.
Open the lid, remove the chicken breasts, and shred them with two forks until they’re nicely pulled apart. Return the shredded chicken to the slow cooker.
Add the softened cream cheese to the slow cooker and stir gently until it melts into the broth, creating a rich, velvety texture. Continue stirring until the soup is smooth and creamy.
Taste the soup and adjust the seasoning with more salt and pepper if needed. Squeeze in fresh lemon juice to brighten the flavor.
Let the soup sit uncovered for a few minutes to thicken slightly, then garnish with chopped herbs before serving hot in bowls.