Combine all ingredients in glass bowl. Mix well to combine. Refrigerate at least 1/2 hour or until ready to use.
Soak Chicken cutlets in water and vinegar for about 10 minutes.
Rinse several times with cold water, pat dry and transfer to mixing bowl or ziploc bag.
To the chicken add, garlic, juice of 2 limes, olive oil, oregano, salt and black pepper to taste. Mix well and let marinade for a least 1/2 hour (the longer it marinades, the better it will taste). If marinating more than one hour, refrigerate, but bring to room temperature before grilling.
Preheat indoor or outdoor grill to medium high heat. (If using indoor grill cook chicken in batches, 2 or 3 at a time).
Add chicken and cook 3 minutes per side. Let chicken rest for 10 minutes, then dice in small pieces.
Add chicken to flour tortillas, top with Pico de Gallo and Shredded Cheddar Cheese.
Roll the tortillas up, place on greased baking sheet seam side down.