Heat the oil in a medium saucepan over medium heat. Add the onion and saute for about 3 minutes. Add the garlic, tomatoes, broth, corn and chilies. Bring the liquid to a simmer then cover the pan and cook gently over low heat for 15 minutes. Meanwhile rinse and mince the cilantro.
While whisking constantly, slowly drizzle the cornmeal into the simmering soup, Simmer gently uncovered until thickened, about 10 minutes. Stir the bottom on occasion to make sure the cornmeal isn't sticking.
Season the soup to taste with salt and pepper. Right before serving stir in the lime juice. Portion out and garnish if you wish with cheddar cheese, cilantro and chopped green bell pepper.
VARIATION -You can enrich it with cubed smoked ham or roasted pork