In a small bowl, whisk together the lemon zest and juice, oregano, oil, 2 teaspoons coarse salt and 1 teaspoon pepper. Divide the marinade between 2 large re-sealable plastic bags. Divide the chicken between the bags; shake to coat. Let marinate at room temperature for 30 minutes, turning bags occasionally.
GRILL THE CHICKEN:
Preheat the grill to medium; lightly oil the grates. Remove the chicken from its marinade, and pat dry with paper towels. Place the chicken on the grill. Cover and cook until lightly browned and cooked through, about 8 to 10 minutes. Turn the chicken over, cover and cook until chicken is cooked through (an instant-read thermometer should read 175° when inserted into the thickest part of the chicken). If the chicken is browning too quickly, move to cooler parts of grill or turn grill to low heat.
Transfer the chicken to a cutting board. Tent with foil; let rest 10 minutes. Meanwhile, place lemon halves on the grill, cut side down; cook until slightly charred, 8 to 10 minutes. Serve chicken breasts with grilled lemon halves. Garnish with fresh oregano sprigs, if desired.
Chicken grills up best when it's an even thickness throughout the breast. Take the time to pound out the breasts slightly (between two pieces of plastic wrap) to even out the thickness.