MARINADE: Combine 3/4 cup vegetable oil, 1/4 cup + 2 tablespoons soy sauce, 3 tablespoons Worcestershire sauce, 1/4 cup red wine vinegar, about 3-4 tablespoons lemon juice, 1 teaspoon lemon zest, 1/2 tablespoon black pepper, 2 teaspoons minced parsley, 3 tablespoons yellow mustard, 1-2 teaspoons minced garlic (for a more intense flavor use 2), and 1 tablespoon honey in a large bowl.
RESERVE: Set aside 1/3 cup of the marinade and save it for basting later.
PREP CHICKEN: Remove fat from the chicken and pound the chicken to an even width (about 1 inch wide everywhere.) If breasts are very thick, cut them in half to get them 1 inch thick. Prepping the chicken like this will ensure even grilling and make sure more chicken gets all those great marinade flavors.
MARINATE: Place the chicken in the marinade and marinate for at least 30 minutes to 6 hours. The chicken is best at 4-6 hours. Too much longer and it tends to get salty/cooked by the vinegar and lemon.
PREP GRILL: Make sure your grill grates are clean and greased. To grease, dredge a paper towel in vegetable oil and holding it with tongs, rub it all over the grate. Grease, once the grill has been preheated to about 375-450 degrees F. Don't go hotter than 450 to avoid drying out the chicken.
GRILL: Grill the chicken until completely cooked through (about 4-6 minutes per side depending on the heat of the grill and thickness) Chicken should register 160 degrees F at its thickest part (carry-over heat will bring it to 165 degrees). For 1-inch-thick breasts grilled at 400 degrees, it takes generally 5 minutes on the first side and 4 minutes on the other side.
BASTE: Generously brush chicken with the reserved marinade mix as it grills. Keep grill closed as much as possible though.
OPTIONAL: For a quick lemon-butter sauce to serve over the chicken, combine 3 tablespoons melted butter, 3 tablespoons lemon juice, 1-2 teaspoons lemon zest, 3 tablespoons olive oil, and 3 tablespoons honey in a small bowl. Add some pepper and parsley if desired. Serve with the chicken.