Peel carrots and cut in half lengthwise, then place at the bottom of the slow cooker. Spread half the butter over carrots, place a sprig of rosemary on top and add garlic cloves. Add water and generously season with salt and pepper.

Place chicken over vegetables, adding a rosemary sprig to the cavity. Pour honey over chicken and generously season with salt and pepper. Add remaining butter on or around the chicken and top with lemon zest.

Cover and cook on low for 6 hours. If needed, leave on warm for 4 more hours, or until ready to serve.