Grilled Chicken Greek Salad

Name: Grilled Chicken Greek Salad
Ingredients: 1/3 cup extra-virgin olive oil, plus more, for the grill; 2 large boneless, skinless chicken breasts (about 1 1/2 pounds), cut into 1-inch pieces; Kosher salt and freshly ground black pepper; 2 tablespoons fresh lemon juice; 1/2 teaspoon dried oregano; 8 cups chopped romaine lettuce; 1 cup sliced cucumber; 1/2 cup pitted Kalamata olives; 1/4 cup thinly sliced red onion; 8 ounces feta cheese, broken into large chunks; 2 pieces pita bread, for serving