Slice zucchinis into 1/8-inch long strips. Place in large sealable, plastic bag. To zucchini, add the oil, vinegar and salt and pepper, to taste. Seal bag and set aside in cool location or refrigerate until ready to grill.
Set grill to medium heat.
Lay zucchini strips across grill, cook on each side for 3 minutes or until dark grill marks appear. Reserve oil mixture.
Toss spinach in remaining oil mixture, add more salt and pepper, if desired. Put spinach in serving bowl or portion on each plate separately. Lay cooked zucchini strips across the top.