In a large sauté pan heat 2 teaspoons olive oil, add half the onion, the garlic and cook for 1-2 minutes. Add the chicken, peppers and lime juice. Cook chicken 7-8 minutes or until chicken is cooked through. Set aside. Once chicken is cool enough to handle, take 2 forks and shred chicken. Add chopped cilantro and 1/2 teaspoon salt. Set aside.
In a large bowl, add Masarepa, lime zest, 1 ½ cups water, 2 teaspoon olive oil and ½ teaspoon salt Stir to form a stiff dough. Transfer dough to clean, dry work space and knead dough for about 30-40 seconds or until smooth. Set aside for 3-4 minutes to rest. Form into 8 equal size balls. Flatten the balls with the palm of your hands to create 1/4 inch thick discs.
In a large sauté pan, heat 2 teaspoons olive oil (you may need a little more during cooking) until very hot, add dough discs, and lower the heat to medium-low. Cook arepas for about 8-10 minutes per side or until cooked through.
When cool enough to handle, cut Arepas horizontally in half. Place chicken mixture and cheese on the bottom half of Arepas. Top with other half and serve.