Trim any visible fat and membranes from the chicken breasts.
Make shallow crosswise slits about 1/2 inch apart along each breast to help the marinade penetrate.
In a bowl, whisk together the olive oil, lemon juice, lemon zest, Greek seasoning, poultry seasoning, dried oregano, and black pepper to form the marinade.
Place the chicken in a single layer in a large resealable plastic bag and pour in the marinade; seal the bag and press to coat the chicken evenly.
Marinate in the refrigerator for 6–8 hours or up to all day. If you have less than 6 hours, increase the lemon juice slightly.
When ready to cook, remove chicken from the fridge and pour the bag contents into a colander to drain; let the chicken come toward room temperature if time allows.
Preheat the grill to medium-high and oil the grates or spray with nonstick spray.
Place chicken on the grill top side down on the diagonal to the grates and cook about 4 minutes, then rotate each piece to create diagonal grill marks and cook another 4 minutes.
Flip the chicken and cook the other side about 4–8 minutes more, until the chicken feels firm but not hard and registers 165°F (75°C) with an instant-read thermometer.
Transfer the chicken to a plate or cutting board and let rest a few minutes before serving or slicing.
Use leftovers in salads, wraps, or other dishes as desired.