Preheat a grill to medium-high heat.
In a mixing bowl, combine the lemon juice, olive oil, oregano, black pepper, and salt. Whisk until combined.
Place the chicken breasts in the marinade and let them sit for 15 minutes. This will help tenderize the chicken and give it a great flavor.
Add the cedar chips to the preheated grill. Place the marinated chicken breasts on the grill and cook for 8-10 minutes per side, or until an internal temperature of 165 degrees F is reached.
Once done cooking, let the chicken rest for 5 minutes before serving.
Serve the cedar-grilled lemon chicken with your favorite side dishes!