Place the chicken breasts in the bottom of the slow cooker.
In a bowl, stir together the ranch seasoning mix, cream of chicken soup, and chicken broth until smooth. Pour this mixture over the chicken.
Scatter the cubed cream cheese evenly over the top.
Cover and cook on low for 6 hours or until the chicken reaches an internal temperature of 165 degrees.
About 30 minutes before the chicken is done, place the potatoes in a large pot and cover with water. Bring to a boil and cook until fork tender, about 15 minutes.
Drain the potatoes, then return them to the pot. Add the butter, milk, salt, and pepper. Mash until smooth.
Shred or slice the chicken and stir it into the sauce in the slow cooker. Serve the chicken and sauce over the mashed potatoes.