In a large bowl, combine the olive oil, lemon zest, lemon juice and parsley. Stir to combine. Transfer half of the marinade to a small bowl. Add the shrimp to the large bowl and toss to coat the shrimp with the marinade. Cover and refrigerate for 15 minutes. (Do not marinate longer or the shrimp will become tough.)

Remove the shrimp from the refrigerator and thread onto skewers.

Heat a grill over medium heat. Grill the shrimp until the shrimp are opaque, 4 to 6 minutes, turning once during cooking time. Transfer to a serving dish and drizzle with the reserved marinade.