In a large bowl or resealable plastic bag, combine vodka, lemon juice, sugar, olive oil, salt, and pepper. Stir to dissolve sugar and salt. Add the chicken and mix to coat. Cover bowl or seal bag and refrigerate for 2 to 4 hours.

Preheat oven or grill to 400 degrees.

If cooking in oven, line a 9x13 baking pan with two layers of foil. Arrange chicken in a single layer in the pan, and pour the marinade evenly over all. Bake until meat has browned, about 1 hour and 15 minutes.

If grilling, arrange on grill and baste often with marinade. Grill for about 4-6 minutes per side.