In large glass bowl, mix together lime juice, olive oil, shallot, garlic, lime peel, oregano, salt, cumin and pepper. Place chicken in mixture, turning to coat completely. Cover and refrigerate several hours or overnight, turning chicken several times.
At cooking time, pour off marinade and place chicken on rotisserie spit. Cook about 1 1/2 hours or until drumsticks move easily in their sockets and juices run clear. When done, a meat thermometer inserted into the thigh will register 180°F. Remove chicken from rotisserie and place on rack; let sit about 10 minutes. Move chicken to platter and discard strings. Garnish with lime slices and cilantro sprigs