Bring a large pot of generously salted water to a boil. Add the orzo and cook according to the package directions for al dente. Drain and rinse under cold water until cool. Place in a large bowl; set aside.
Meanwhile, for the dressing: Whisk the olive oil, vinegar, oregano, garlic, salt and a few grinds of pepper in a medium bowl until combined.
Add the tomatoes, olives, feta, basil, chickpeas and onion to the orzo. Drizzle in all but 2 tablespoons of the dressing and stir to combine. Refrigerate for at least 1 hour or overnight.
Toss the shrimp in a bowl with the reserved 2 tablespoons dressing and set aside to marinate for 10 minutes. Meanwhile, soak 6 wooden skewers in water to prevent them from scorching.
Preheat the broiler. Thread the shrimp on the skewers, season with salt and place on a baking sheet. Broil for 2 minutes, then flip the skewers and broil until the shrimp is pink and cooked through, about 1 more minute. Top the orzo mixture with the shrimp and more feta and basil.
