Preheat a grill pan or preheat a gas or charcoal grill.
Season the chicken and shrimp with the dried oregano, salt and pepper. Drizzle with olive oil. Grill the chicken for 5 to 6 minutes each side until cooked through. Grill the shrimp for 1 to 2 minutes on each side until pink and cooked through.
In a small skillet, heat the olive oil over medium-high heat. Add the pancetta and cook, stirring constantly until browned, about 6 to 8 minutes. Drain on paper towels. Set aside.
In the bowl of a food processor, combine the garlic, parsley, oregano, vinegar, extra-virgin olive oil, and lemon juice. Pulse until smooth. Season with salt and pepper, to taste.
Slice the chicken diagonally and arrange on a large serving platter with the shrimp. Drizzle with the chimichurri and sprinkle with the pancetta.