Heat 1 cup oil in medium skillet over medium heat. Working in batches, add tortilla strips; fry until golden, about 2 minutes. Transfer to paper towels; drain.
Mix broth and next 4 ingredients in large saucepan; bring to boil. Reduce heat; simmer 15 minutes. Add lime juice; season with salt and pepper. (Tortilla strips and soup can be made 1 day ahead. Store strips airtight at room temperature. Cover soup and chill; rewarm before continuing.)
Meanwhile, heat remaining 2 tablespoons oil in heavy large skillet over medium-high heat. Sprinkle chicken with salt and pepper. Add chicken to skillet; sauté 3 minutes. Add tomato, bell pepper and onion. Sauté until chicken is cooked through, about 2 minutes longer.
Place 1 lime slice in each of 6 bowls. Ladle soup over. Mound tortilla strips and chicken mixture in center of each.