Heat 1 tablespoon olive oil in a medium saucepan over medium-high heat. Add the onion, celery and a pinch of salt and cook, stirring occasionally, until softened, 5 minutes. Stir in 3 minced garlic cloves and 1 tablespoon oregano; cook 30 seconds.
Add the rice, olives, lemon quarters, 1 1/2 cups water and 1 teaspoon salt to the pan. Bring to a boil, then reduce the heat to low and stir. Cover and simmer until the liquid is absorbed and the rice is tender, about 17 minutes.
Meanwhile, heat the remaining 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Season the chicken with salt and pepper, add to the skillet and cook, turning once, until browned, about 8 minutes. Add the remaining 2 minced garlic cloves and 1 tablespoon oregano and cook, stirring, until the garlic is softened, about 10 seconds. Add the lemon juice and scrape up any browned bits with a wooden spoon. Add the chicken broth, bring to a simmer and cook until reduced by about half and the chicken is cooked through, about 5 minutes.
Fluff the rice with a fork. Divide among plates, top with the chicken and pan juices and sprinkle with the chives.