Add the chicken breasts, celery, carrot, potato, and chicken stock. Bring to the boil, then turn down to simmer for about 20 minutes until the chicken has cooked through.
Remove the chicken breasts using a slotted spoon and set aside on a chopping board.
Stir the milk and cream cheese into the pot with the vegetables. Use a hand whisk if necessary, until there are no lumps. Then using the wooden spoon press the potatoes to side of pan to break them down.
Shred the chicken breasts on the chopping board using two forks.
Stir the shredded chicken and parsley into the pot. Season to taste with salt and pepper. Serve.