Cut chicken in half lengthwise. Blend butter and mustard together. Rub chicken inside and out with this mixture. Place chicken, skin side down, in baking dish with tight-fitting cover.
Preheat oven to 375 degrees. Combine orange juice and brown sugar, stirring until sugar is completely dissolved. Pour over and around chicken. Cover and bake for 30 minutes.
Turn chicken over, baste with pan juices, and continue to bake, uncovered, for 20 minutes longer, basting occasionally.
Remove chicken to heated platter and keep warm. Mix cornstarch with water. Stir this into juices from pan. Cook over low heat, stirring constantly, until thickened. Remove from heat, stir in vodka, and pour sauce over chicken.
Can be cooked in a crockpot, place chicken on the bottom and cover with sauce then cook on Low for 6-8 hours.