Prepare a 9 x 13-inch baking dish and set it on the counter.
In the dish, whisk together 1/2 cup extra-virgin olive oil, the juice of the lemons (about 1/4 cup used in the marinade), the lemon zest (about 2 teaspoons), minced garlic, chopped parsley, dried oregano, salt, dried thyme, ground black pepper, and crushed red pepper if using.
Add the chicken pieces to the dish and turn them to coat thoroughly in the marinade.
Cover the baking dish with plastic wrap and refrigerate for at least 30 minutes and up to 4 hours.
To grill: preheat the grill to medium (about 350–400°F). When hot, grill the chicken 5 minutes per side or until cooked through.
To bake: preheat the oven to 400°F. Line a rimmed baking sheet with parchment paper, arrange the chicken pieces so they do not touch, and bake 15–20 minutes or until the thickest piece is cooked through.