Preheat oven to 400 degrees F or heat your outdoor grill.
Slice off ends of zucchini and discard.
Make slices in zucchini crosswise but don't cut through bottom of zucchini.
If Baking in oven, place zucchini on a foil lined baking pan.
Brush zucchini with oil and bake 20 -25 minutes until tender.
If Grilling: Wrap 2 pieces in foil and close tightly. Grill on medium high heat until tender but not too soft, about 15-20minutes.
Remove from oven or grill to cool slightly.
Cook the bacon until crisp and drain on paper towels. Once cool enough to handle, break into pieces.
Insert a slice of cheese and piece of bacon into zucchini.
Broil 3-5 minutes or grill covered ,with the foil packet opened, for just a minute until cheese is melted.
Top with chives and Parmesan cheese if desired.