Mix lemon juice, olive oil, garlic, oregano, salt, and black pepper in a bowl; pour into a sealable plastic bag. Add the chicken to the bag, coat with the marinade, and squeeze air from the bag before sealing. Refrigerate 8 hours to overnight.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Remove chicken from the marinade and shake off excess. Discard the remaining marinade.
Cook chicken on hot grill until no longer pink in the center and the juices run clear, about 5 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).