Arrange the chicken pieces in a single layer in the slow cooker. Sprinkle with salt and pepper, garlic, and oregano. Add 3/4 cup of the orange juice. Cover and cook on low for 5 hours, or until the chicken is tender.
Remove the chicken to a serving platter. Cover and keep warm. Pour the chicken juices into a small saucepan. Bring to a simmer. In a small bowl, stir together the remaining juice and cornstarch until smooth. Add to the saucepan and cook, stirring, until smooth and thickened, about 1 minute. Stir in zest. Pour the sauce over the chicken. Sprinkle with parsley and serve hot.