(Skip this step if using chicken tenderloins.) One at a time, place the chicken breasts in a sealable plastic bag and, using a meat mallet, pound to an even ½-inch thickness.

Open a 1 gallon zip-lock bag and place in a medium bowl. Add the oil, garlic, lime zest, cumin, oregano, ancho chili powder, smoked paprika and salt into the bag. Mash the outside of the bag with your hands to blend the marinade together. Add the tenderloins or pounded chicken breasts and seal shut, releasing any air in the bag. Using your hands, massage the marinade into meat until evenly coated. Place the bag back in the bowl and place in the refrigerator (the bowl protects against leakage); let the chicken marinate at least 8 hours or up to 24 hours.

Clean the grill and preheat to high.

While the grill heats, cook the peppers. Heat the oil in a large skillet (preferably not non-stick) over medium-high heat. Add the sliced onions, peppers, salt, and sugar; cook, stirring occasionally, until the vegetables start to brown and a brown film forms around edges of the bottom of the pan, 8 to 10 minutes. Add ¼ cup of water to the pan; scrape the bottom of the pan with a wooden spoon to release any browned bits. Continue cooking for 3 to 4 minutes, until the water is evaporated and the pan starts to brown again; add ¼ cup more water and cook a few minutes more, until the vegetables are tender-crisp. Season to taste with more salt and sugar if necessary. Set aside.

Oil the grates on the grill. Grill the chicken, covered, for 2 to 3 minutes per side. Do not overcook. Let the chicken cool slightly, then transfer to a cutting board and cut into ½-inch strips.

Arrange the chicken and peppers on a serving platter. To warm the tortillas: stack 4-6 tortillas on a plate and cover them with a damp paper towel, then microwave for 30 seconds to 1 minute. Repeat with the remaining tortillas. Serve with the chicken, peppers and optional accompaniments.