Spread the potatoes in a 6-quart slow cooker and arrange the chicken breasts on top.
Whisk the condensed soup, broth, ranch seasoning and black pepper until smooth and spoon it over the chicken.
Cover and cook on low for 3 1/2 hours.
Add the green beans around the chicken, cover and cook until the breasts reach 165°F and the potatoes are tender, 30 to 60 minutes more.
Transfer the chicken and vegetables to a platter and turn off the cooker.
Stir the sour cream into the hot sauce until smooth and spoon it over the dinner.