Slice the zucchini in half, lengthwise and then cut the pieces in half again. You will have 8 long slices about 1/2" thick. Place sliced zucchini in a gallon sized zippered plastic storage bag.
In a small mixing bowl combine olive oil, balsamic vinegar, sugar, Italian seasoning, and fresh ground pepper to taste. Pour the dressing over the zucchini, seal the bag, and move it around to distribute the dressing well. Place the bag in the refrigerator for at least a 30 minutes and up to 4 hours.
If grilling indoors, place stove top grill over medium-high heat. Lightly coat grill with olive oil and grill zucchini for approximately 2 to 3 minutes on each side or till fork tender but not mushy. If grilling outdoors, prepare your grill and grill the zucchini with cover open as directed for indoor cooking.