In a medium bowl, combine mayo, lemon juice, vinegar, garlic, and oregano.
Pour 3/4 cup of marinade in a ziploc bag (refrigerate remaining marinade).
Add chicken. Squeeze out air as much as possible before sealing bag.
Toss and turn the chicken in the bag to make sure pieces are coated in marinade.
Place bag in refrigerator for at least 3 hours, overnight is ideal.
Remove chicken from ziploc bag, and discard.
Grill chicken on your outdoor grill over medium heat for 5 minutes, turn and baste with reserved marinade, and grill for another 4-9 minutes or until chicken is done.
If using and indoor grill, cook chicken for 6-9 minutes or until chicken is done, basting half-way through.