Combine the lime juice, garlic, cilantro, pepper, 1 teaspoon of salt, and 6 tablespoons of olive oil in a large bowl. Add the chicken, cover the bowl, and let the chicken marinate in the refrigerator for a least 1 hour or overnight.
Heat a barbecue grill to 350°F.
Depending on the size of the chicken breasts grill for 6 to 8 minutes on each side, or until the internal temperature reaches 165°F. Allow the chicken to rest for 5 to 10 minutes after removing it from the grill. Then slice into 1/2-inch strips.
While the chicken is cooking, place all the sliced vegetables into a bowl and drizzle with the remaining tablespoon of olive oil. Add two pinches of salt and toss to coat. Place the vegetables on the grill for about 15 minutes, turning halfway through.
Place the tortillas on the grill to heat through, and serve.