Put the potatoes into a slow cooker and pour the broth on top. Cover and cook on high for 4 hours (or on low for 8 hours), until the potatoes are cooked and soft.
Drain the potatoes, reserving some of the broth, and return them to the slow cooker. Add the buttermilk, sour cream, butter, salt and pepper to taste and mash with a potato masher. Stir in the chives and keep warm until ready to serve. It's best to eat right away, but if you're eating them later and the potatoes get dry, add some of the reserved broth to soften them.