Spread the tortilla slivers on a nonstick baking sheet or on a piece of foil and bake in a 400°F oven or toaster oven until lightly browned, about 4 minutes. Let cool on a plate.
Heat the olive oil in a large saucepan. Add the onion, garlic, and chili slices and cook over medium heat until lightly browned, about 5 minutes. Stir in the chicken stock, lime juice, chicken, and tomato. Gently simmer the soup until the chicken is cooked. Add salt and pepper to taste and extra lime juice if desired: The soup should be highly seasoned. Stir in the cilantro. Ladle soup into bowls and sprinkle with toasted tortilla strips.