Step 1

Bring the chicken broth, chicken breasts, red onion, garlic, oregano, salt, pepper, and thyme to a boil in a large pot; reduce heat to medium-low and simmer until the chicken breasts are no longer pink in the center and the juices run clear, 15 to 20 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Remove the cooked chicken to a cutting board and shred into bite-sized strips; return to the simmering pot.

Step 2

Heat the oil in a skillet over medium heat; cook the green onions and green chile pepper in the hot oil until tender, about 5 minutes. Stir the tomatoes into the mixture and continue cooking until soft, about 5 minute more; pour the mixture into the pot with the chicken soup. Season with the salt; return the soup to a simmer. Add the lime juice and 1/2 a lime; cook another 10 minutes. Remove the pot from the heat and remove the lime half; stir in the cilantro to serve.