In a large bowl mix together the 1 TBSP olive oil, salt, and black pepper. Add the chicken strips to the bowl and toss to coat.
Heat a skillet over medium heat. When the pan is hot add the chicken and cook, stirring occasionally, until cooked through, about 7 minutes. Transfer the cooked chicken to a plate and set aside.
In a large mixing bowl toss together the cooked chicken, cucumber, lettuce, tomatoes, olives, onion, pepperoncini, and feta.
Make the GARLIC VINAIGRETTE DRESSING: In a small bowl whisk together the olive oil, vinegar, Dijon, garlic, salt, and pepper until well combined.
Drizzle the dressing in the bowl over the chicken and vegetables and stir to combine.
Warm the tortillas so theyre more flexible then lay the tortillas out flat. Add the chicken and vegetable mix to the bottom half of the tortilla then fold the bottom of the tortilla up and over the mix. Make two folds on either side of the large fold and roll it up tight.