In a medium saucepan, heat the olive oil over medium heat. Add the onion and garlic and cook until softened, about 3 minutes. Add the rice and stir to coat with the oil.
Add the chicken broth and bring to a boil. Reduce heat to low, cover and simmer for 18 minutes.
Remove from heat and let stand for 5 minutes. Fluff with a fork.
In a small skillet over medium heat, melt the butter. Add the lime juice and cilantro leaves, stirring until combined.
Pour the butter mixture over the cooked rice and stir to combine.