Heat vegetable oil in a saucepan over medium heat. Stir rice in hot oil until coated; add green chiles and continue cooking until rice begins to brown lightly, 2 to 3 minutes. Season rice with pepper. Pour broth into the saucepan; bring to a boil. Reduce heat to low, place cover on the saucepan, and cook until the broth is absorbed and the rice tender, about 20 minutes.