In a large pot over medium-high heat, add the vegetable oil; once hot, add the onion, garlic, and jalapenos, and cook for 5 minutes or until the onion has softened.
Place the chicken breasts at the bottom of the pot, then layer in the rest of the ingredients. Stir to combine.
Lower the heat to medium-low and let the soup simmer uncovered for 25 minutes.
Take out the chicken breasts from the pot and shred them using two forks.
Return the shredded chicken to the soup and stir well.
Serve the soup hot in bowls, garnished with crushed tortilla chips, grated cheese, a quarter of a lime, and chopped cilantro.