Prepare the grill for direct cooking over medium-high heat (400° to 500°F).
Place one of the chicken breasts on a work surface between two sheets of plastic wrap. Using a meat mallet or the bottom of a small, heavy skillet gently pound from the center toward the edges until the meat has a uniform thickness of just over ¼ inch. Repeat with the remaining chicken breasts.
In a large bowl whisk the oil, vinegar, oregano, salt, and pepper. Add the chicken breasts to the bowl and turn to coat all sides thoroughly. Cover and let stand at room temperature while you make the sauce.
In a medium bowl combine the sauce ingredients. Set aside.
Brush the cooking grates clean. Grill the chicken, smooth (skin) side down first, over direct medium-high heat, with the lid closed, until no longer pink, 3 to 4 minutes. Turn the chicken over and grill just to sear the surface, about 1 minute more. Remove from the grill and serve the chicken warm with the sauce, raisins, almonds, and dark scallion greens.