Peel and devein shrimp. Combine oil and next 4 ingredients in a large heavy-duty, zip-top plastic bag. Add shrimp; seal bag, and marinate in refrigerator 1 hour, turning once.
Soak 8 (6") wooden skewers in water to cover at least 30 minutes.
Remove shrimp from marinade, discarding marinade. Wrap 1 piece prosciutto around each shrimp. Thread 2 shrimp onto each skewer. Place skewers on rack of a lightly greased broiler pan. Broil 5 1/2" from heat (with electric oven door partially opened) 7 to 9 minutes or until shrimp turn pink, turning once.