Place the diced potatoes, chicken breasts, ranch seasoning mix, chicken broth, diced onion, minced garlic, salt, and black pepper into the slow cooker.
Stir gently to distribute the seasoning, then cover and cook on low for 6 hours.
Remove the chicken breasts from the slow cooker and shred them with two forks.
Return the shredded chicken to the slow cooker and stir in the heavy cream.
Continue cooking on low for 20 more minutes until the soup is heated through and slightly thickened.
Turn off the heat and stir in the chopped fresh parsley and chives just before serving.