In a heavy medium saucepan, heat the oil over medium heat. Add the chorizo and cook, stirring occasionally, until lightly browned, about 4 minutes. Add the rice and stir for 1 minute to coat. Stir in 1-1/2 cups water and the salsa and bring to a boil, stirring once or twice. Cover the pot and simmer on low heat for 20 minutes.
Fluff the rice and stir in the corn. Remove from the heat, cover and let stand for 5 minutes. Stir in the olives and cilantro.
