Marinate shrimp for 1 hour in leftover Grilled Whole Rosemary Chicken marinade (don't worry; you'll be cooking the shrimp). Meanwhile, juice limes and lemon, and chop tomatoes, avocado, and cilantro.
Add shrimp, marinade, and any cooking juices from Grilled Whole Rosemary Chicken to a saucepan and bring to a boil. Simmer 5 minutes or until all shrimp is pink. Meanwhile, prepare another saucepan or metal bowl with 12 ice cubes. Pour shrimp and marinade over ice to cool, adding more ice as necessary to chill.
Drain shrimp, discarding marinade, and add to a serving bowl with tomato, avocado, cilantro. Add oregano, lemon and lime juice, Worcestershire, and hot sauce if using, and mix. Serve right away or refrigerate for 1 hour before serving.