In a bowl, whisk together the olive oil, freshly squeezed lime juice, fajita seasoning, and minced garlic until well combined. Place the chicken breast strips into a zip-top bag or shallow container and pour the marinade over them, making sure all pieces are evenly coated. Seal the bag and refrigerate for at least 20 minutes—I prefer 45 minutes to an hour for deeper flavor penetration, but even 20 minutes makes a noticeable difference. While the chicken marinates, you can prep your vegetables.
While the chicken marinates, prepare all your vegetables. Seed the bell peppers and cut them in half lengthwise for easy grilling—keeping them in large, flat pieces prevents them from falling through the grate. Slice the white onion into 1/2-inch thick rounds, leaving the root end intact so the layers stay together during cooking. Roughly chop the fresh cilantro and set aside for garnish. Having everything prepped before you heat the grill keeps the cooking process smooth and prevents any burned items while you're still cutting.
Preheat your grill to medium-high heat (around 400-425°F if using a gas grill). Once hot, oil the grate generously using an oil-soaked paper towel held with tongs to prevent sticking. Let the grill stabilize for a few minutes so the chicken and vegetables develop a nice char. Having the grill properly heated and oiled is essential for creating those signature caramelized grill marks that make fajitas so appealing.
Remove the marinated chicken from the refrigerator and arrange it on the grill along with the pepper halves (skin-side down first) and onion rounds in a single layer. Grill for 6-7 minutes without moving, allowing the chicken and vegetables to develop a golden char. Flip everything and continue cooking for another 8-12 minutes until the chicken reaches an internal temperature of 165°F and the vegetables are tender and lightly charred. I like to use tongs to occasionally rotate the vegetables for even browning rather than constantly flipping them.
Transfer the grilled chicken and vegetables to a warm plate and let them rest for 5 minutes—this allows the juices to redistribute, keeping the chicken moist. While resting, place the tortillas directly on the grill grates for about 1 minute per side, just until they're warmed through and slightly charred. Stack them in a clean kitchen towel to keep them warm and pliable for serving.
Slice the rested chicken and grilled vegetables into thin strips for easy serving. Arrange the warm tortillas on a platter alongside the sliced chicken and vegetables, allowing guests to build their own fajitas. Garnish with the chopped cilantro and serve immediately while everything is still warm.