Heat oil in a large skillet over medium-high heat. Once hot add chicken, season with salt and pepper, and saute until cooked through, about 6 minutes, adding in lighter portions of the green onions and garlic at last 1 minute of cooking. Stir in broth, green onion greens, green chilies, lime zest, lime juice, black beans and season with salt and pepper to taste. Bring mixture to a boil, add rice, fully immerse rice in broth, and allow to boil 20 seconds, then remove from heat and immediately cover with a lid. Let rest 5 - 6 minutes.
If needed, return pan to medium heat and cook and toss 1 minute to allow rice to absorb excess moisture. Remove from heat, toss in cilantro and let rest uncovered 3 minutes.