If using chicken tenderloins, you can skip this step. Place each chicken breast in a large resealable bag and gently pound with a meat mallet until evenly flattened to about ½-inch thick. This helps the chicken cook evenly.
Add the ¼ cup avocado oil or olive oil, 3 cloves minced garlic, 1 tablespoon lime zest from 2 limes, 1 teaspoon cumin, ¾ teaspoon oregano, ¾ teaspoon chili powder, ½ teaspoon smoked paprika, and 1 teaspoon salt to a 1-gallon zip-top bag. Press and mix the ingredients together from the outside of the bag until the marinade is combined. Add the chicken, remove any excess air, and seal the bag. Massage the marinade into the chicken until evenly coated, then refrigerate for at least 2 hours or up to 24 hours.
Just before heating the grill, begin to prep the onion and peppers. Heat oil in a large skillet over medium-high heat. Add the sliced onions, peppers, ¼ teaspoon salt, and ½ teaspoon sugar. Cook, stirring occasionally, until the vegetables begin to soften and develop browned bits on the bottom of the pan, about 8–10 minutes.
Pour in ¼ cup water and use a wooden spoon or silicone spatula to scrape up any browned bits from the pan. Continue cooking for 3–4 minutes until the water cooks off and the vegetables begin browning again. Add another ¼ cup water and cook a few more minutes, until the peppers and onions reach your preferred texture. For softer, deeply caramelized vegetables with extra char, cook them a little longer. If you prefer the peppers and onions more crisp-tender, remove them from the heat sooner.
While the onions and peppers are cooking, clean and preheat the grill to high heat.
Lightly oil the grill grates. Grill the chicken with the lid closed for 2–3 minutes per side, or until cooked through. Avoid overcooking. During the last minute or two, place the tortillas directly on the grill and cook for about 15–30 seconds per side, just until warmed and lightly charred. Let the chicken rest for a few minutes, then slice into ½-inch strips.
Arrange the sliced chicken and peppers on a serving platter. Serve with warm tortillas and your favorite toppings.