Heat the slow cooker on the low setting.To the slow cooker, add the chicken stock, ham, mushrooms, onion, tarragon, salt and pepper.
Cover and let cook.In a large saute pan, over medium-high heat, pan-sear the chicken in butter and garlic until browned.
Add the chicken, along with all drippings from the pan to the slow cooker.Next, add the heavy cream, sour cream, Parmesan cheese, and Swiss cheese.
Cover and cook on low for 6 hours.