Wrap grapes with small pieces of prosciutto about 1-inch wide by 3-inches long. Skewer each grape with a pick, securing prosciutto. Repeat until all grapes are used. Set aside.
In small bowl, combine oil, rosemary, garlic and pepper. Lightly brush wrapped grapes with seasoned oil. Grapes can be prepared to this point, refrigerated and then cooked when ready to serve.
Heat gas grill to medium, then grill grapes lightly, about 2 minutes per side. Prosciutto should be crisp, and grapes warmed through. Drizzle with additional oil if desired and serve hot.