To make the dressing, place all the ingredients in a small bowl and stir well to combine. Taste and adjust seasoning to your liking. Cover and store in fridge for up to 5 days.
Layer half the sauerkraut in the bottom of a greased 5-6 quart slow cooker. Drizzle with ⅓ of the dressing.
Season the chicken on all sides with salt and pepper. Place the chicken breasts on top and spread half the mustard over the chicken. Top with the remaining sauerkraut and drizzle another ⅓ of the dressing over all and reserve the remaining dressing and mustard for serving.
Cover and cook on low for 4 hours, or until chicken is cooked through and tender.
To serve, place each breast on a plate. Divide the sauerkraut over top the chicken. Top each with a drizzle of the remaining dressing and mustard.
Store extras in an airtight container in the fridge for up to 5 days. To reheat, place in a casserole dish in a 350 degree F oven for 5 minutes or until heated through.