Heat olive oil in a large saucepan over medium-high heat.
Add onion to pan; saut 2 minutes. Stir in garlic and jalapeo; saut 1 minute.
Add chicken, black pepper, and broth; bring to a boil. Reduce heat, and simmer 5 minutes. Stir in hominy; bring to a boil. Cook 5 minutes. Ladle about 1 1/2 cups soup into each of 4 bowls; top each serving with 2 tablespoons radishes and 1 1/2 teaspoons cilantro.