In a large skillet, heat 1 tablespoon of the oil over medium-high heat. Add chicken and cook, turning once, until no longer pink inside, 6 to 8 minutes per side. Transfer chicken to a cutting board and let cool.

In a large pot, heat remaining oil over medium heat. Add onion, garlic, and tomatoes. Cover and cook until onion is softened, 4 to 6 minutes. Add chicken broth and lime juice.

Dice cooked chicken and add to the pot. Cover and bring to a boil over medium heat. Reduce heat to low and simmer for 10 minutes. Ladle into individual bowls and garnish with equal amounts of tortilla chips, avocado, and green onion.