In a large pot, bring 5 cups of water to a boil. Add the chicken breast, 5 cilantro sticks, ¼ onion, 1 garlic clove, and ½ teaspoon of salt. Allow it to simmer for approximately 15 minutes or until the chicken is cooked through.
While the chicken is cooking, blend the tomatoes, 1 garlic clove, ¼ onion, and 1 cup of water until smooth.
In a separate pot, heat 1 teaspoon of olive oil over medium heat. Add the tomato sauce and cook for about 5 minutes, stirring occasionally.
In another pot, heat 2 teaspoons of olive oil. Add the fideo and sauté until they turn a light golden brown.
Once the chicken is cooked, remove it from the broth, along with the cilantro, onion, and garlic. Shred the chicken.
Add the chicken broth to the pot with the fideo, followed by the tomato sauce and the remaining cilantro on top. Allow it to boil for about 8 minutes or until the fideo is cooked.
Take off the cilantro sticks. Stir in the shredded chicken and add salt to taste.
Serve hot, garnished with queso fresco or Parmesan, if desired. Squeeze a bit of lime juice for an extra burst of flavor.