1. Place a piece of waxed paper or plastic wrap on a countertop or cutting board. Place one chicken breast on top and cover with another piece of waxed paper or plastic wrap. With a mallet, hammer, or other pounding device, pound the chicken breast 1/8 inch thick. Continue in the same way until all the breasts are flattened. Set aside until ready to cook, or cover and refrigerate for up to 2 days.
2. When ready to cook the fajitas, finely grate the onion. In a large nonreactive dish, mix the onion and its juice with the orange juice and soy. Remove the waxed paper or plastic wrap, and place the chicken in the onion-orange-soy mixture. Turn to coat both sides. Set aside to marinate for at least 15 minutes and up to 45, turning once or twice.
3. If grilling, prepare a charcoal fire and allow the coals to bum until they are mostly covered with white ash and a few red spots show through here and there. This will take about 40 minutes. When the fire is ready, place the chicken breasts on the grill rack directly above the coals. Cook until no longer pink but still moist in the center, about 1 to 2 minutes on each side.
If frying, divide the oil between 2 large frying pans and set over medium-high heat until the oil begins to smoke. (You can use 1 frying pan to save on dishes and cook the fajitas in several rounds.) Add as many chicken breasts as will fit in one uncrowded layer. Cook until no longer pink but still moist in the center, about 1½ minutes on each side. Remove and drain off any liquid from the pan. Continue cooking another round until all of the breasts are cooked.
4. Cut the chicken into thin strips.
5. To assemble place about 1/3 cup of chicken in the middle of a tortilla. Top with some shredded lettuce, sour cream, and Green Olive-Cilantro Salsa. Fold and serve.