Heat oil in large skillet over medium-high. Add chicken livers, and cook, stirring constantly, until browned, about 3 minutes. Stir in onion, bell pepper, celery, garlic, Creole seasoning, salt, and pepper,and cook, stirring occasionally, until vegetables are softened and beginning to brown, about 7 minutes.
Add 1/4 cup of the chicken broth, and cook over medium-high 2 minutes, stirring and scraping often to loosen browned bits from bottom of skillet. Stir in duck confit, rice, oregano, and remaining 3/4 cup chicken broth, and cook, stirring occasionally, until liquid is absorbed and rice and confit are heated through, about 4 minutes. Sprinkle with celery leaves, and serve immediately.