In a large ziplock bag, combine the chicken, Greek rub, garlic, oil, vinegar, water, and lemon slices. Seal the bag and shake to thoroughly coat the chicken in the marinade.
Refrigerate the bag for 12 to 24 hours, allowing the flavors to penetrate the chicken.
Preheat your grill to 425°F.
Remove the chicken from the marinade and pat dry with a paper towel to prevent flare-ups on the grill.
Place the chicken pieces directly on the grill. Turn every 6 to 7 minutes to ensure even cooking and prevent burning.
Grill the chicken for approximately 25 minutes, checking for an internal temperature of at least 165°F with a meat thermometer.
Once the chicken reaches the correct temperature, remove from the grill and serve immediately with your preferred sides.