Add chicken to a pot, cover with water by about an inch and bring to a boil over medium-high heat. Immediately turn down to a simmer and simmer for 12 to 15 minutes until tender. If desired, the resulting broth can be used in making the arepas. Remove chicken from broth and shred. Reserve a little of the broth to finish the dish and If desired, the remainder of the broth may be saved and used in making the arepa

In the meantime, heat oil in a skillet over medium heat; add cook and stir onion for about 3 minutes. Add red bell pepper; cook and stir until onion and pepper are softened, several more minutes. Add garlic; cook and stir until fragrant, about 1 minute.

Add the shredded chicken and a tablespoon or two of the reserved broth to moisten, the tomato and salt and pepper to taste. Heat through, gently, stirring often to blend flavors until chicken is still moist but most of the moisture is gone from the pan and the tomatoes have dissolved into the mixture, several minutes. Taste and adjust for salt and pepper and add a squeeze of lime or a little sprinkle of vinegar.

Serve inside still warm and split arepas, topped with green sauce, pickled red onions and cheese. Garnish with lime and avocado if desired.