Make the marinade/dressing: Mix together the olive oil, garlic, lemon juice, red wine vinegar, dried oregano, and pepper in a small bowl or container. Pour half the mixture into a large bowl, container, or sturdy zipper-top plastic bag, and add 1 tablespoon salt. Pour the rest into a small container, and add the fresh oregano and salt. Save this for the dressing.

Place the chicken breasts into the marinade container and turn to coat well. Cover or seal the marinade, and marinate in the fridge for 2 to 6 hours.

Preheat the grill or the broiler. Line a rimmed baking sheet with aluminum foil and spray it with nonstick cooking spray.

Remove the chicken from the marinade and lightly pat dry with paper towels. Discard any remaining marinade. Place the chicken on the prepared baking sheet and grill or broil it until cooked through, about 5 minutes per side. Let the chicken cool to room temperature, then cut it into small cubes.

While the chicken is cooking, cook the orzo according to package directions. Drain and rinse with cool water.

Combine the chicken, orzo, zucchini, scallions, cherry tomatoes, and feta in a large bowl (see Note for more add-in options). Pour over the reserved dressing and toss gently to combine.