Peel strips of zest from half of lemon then cut into fine strips with a knife. Grate the other side of the lemon to make 1 tablespoon zest. Then squeeze the juice from the lemon into a bowl.
In large bowl combine lemon zest and juice, oil, garlic, parsley, thyme, marjoram, salt and pepper.
Add chicken to bowl and spoon marinade over to coat. Cover with plastic wrap and chill 30 minutes or overnight.
Preheat grill, griddle or broiler to medium heat. Put chicken on griddle, reserving marinade. Cook chicken until cooked thru. About 10 minutes per side. Brush with reserved marinade 2 or 3 times during cooking. Sprinkle with reserved lemon strips and serve. Garnish with parsley.