Preheat oven to 200 degrees F. Wrap the pita breads in foil, and put in the warm oven until dinner is ready.
Put the chicken into a shallow dish with sides.Season the chicken with salt and pepper on both sides, to taste.
Mix the lemon zest and juice with the vinegar and then whisk in the oil. Add the oregano, garlic and whisk it again to make sure it's combined well. Pour about half of this dressing over the chicken strips and turn them to coat.
Combine all the veggies in a big bowl and toss well with that leftover dressing (don't pour it all in at once. add some and toss the salad and repeat until you reach the right amt of dressing for your liking). Season with salt and pepper, to taste.
Grill the chicken strips for about 4 to 5 minutes per side. Transfer the chicken strips to your salad bowl/dish when they are cooked through.
Remove the pitas from your oven and unwrap. Cut pitas in half and then arrange them around your salad bowl/dish.
To serve, each person can pile on the grilled chicken and veggies onto their pita and wrap it up!