In a large, non reactive bowl (such as glass, pyrex or ceramic- not plastic or metal), zest the lime. Squeeze in the juice, and add in the oregano, cumin, garlic, chili powder, oil, and salt. Whisk to combine.
Add the chicken breasts turning to coat, cover the bowl and marinate in the refrigerator for at least two hours, and up to 8. When ready to cook, prepare the peppers, onions and avocados, and brush lightly with olive oil.
Prepare your grill and heat to medium. Remove the chicken from the marinade. Cook, turning once, until cooked through. This can take anywhere from 6-12 minutes per side depending on the thickness of the breast. If you have the grill space, at the same time that the chicken is cooking, place the bell pepper pieces and onion slices on the grill (and jalapenos if using). Grill approx. 3-4 minutes per side.
As the vegetables and chicken are done, remove to a cutting board and let rest. Now, place the avocados, cut side down, on the grill over medium-high heat. Let cook without moving until slightly charred, about 3 minutes. At the same time, place the tortillas, wrapped in foil, over very low heat on the grill, or an upper rack if you have one. Turn once, just so the tortillas are warmed through. Remove the avocado to a serving platter, or the cutting board, and wrap the tortillas in a dish towel or tortilla server.
Slice the chicken into strips, and if the peppers are large, slice those into strips. You can serve the chicken, peppers and onions, and grilled avocado right off of the cutting board. Pass with the tortillas, and whatever toppings you prefer, such as sour cream, shredded cheese, or pico de gallo.