Heat the oil in a large pot or Dutch oven over medium heat. Add the onion, bell pepper, jalapeño, garlic, salt, pepper and cook, stirring, until the veggies are tender, about 8 minutes.
Increase the heat to medium-high. Add the drained cans of tomato, broth, oregano and bay leaves, stir and bring to a rapid simmer. Reduce the heat so that it is lightly simmering, over medium-low heat, cover and let the flavors meld for about 10 minutes.
Stir in the chicken and the lime juice and let simmer for 5 more minutes.
To serve, ladle into bowls and garnish with cilantro, some crushed corn tortilla chips, and the cubed avocado.