How to Make It
In a large pot, heat 2 tablespoons of the oil over moderately high heat. Add the tortillas and cook, stirring frequently, until brown and crisp, 3 to 4 minutes. Remove the tortillas from the pot and drain on paper towels.
In a blender, combine the garlic, jalapeño, avocados, lime juice, Tabasco, 1 1/2 cups of the water, 1/2 teaspoon of the salt, and the pepper. Puree until smooth.
Heat the remaining 1 1/2 tablespoons oil in the pot over moderate heat. Add the onion and cook, stirring frequently, until translucent, about 5 minutes. Add the broth and the remaining 2 cups water and 1 teaspoon salt. Bring to a simmer. Stir the chicken into the pot; cook until just done, 2 to 3 minutes. Add the avocado puree. Heat through, about 2 minutes. Serve the soup topped with the crisp tortilla strips.
Even easier: Use broken-up tortilla chips in place of the fried tortilla strips.