Slice each chicken breast in half horizontally to create thinner cutlets. Cover with plastic wrap and pound to an even thickness using a meat mallet or the bottom of a frying pan. Don’t flatten too much, just even things out. Pat dry with paper towels and place the chicken in a large resealable bag.
In a medium bowl, whisk together the honey, oregano, garlic, 1/4 cup fresh lemon juice, olive oil, salt, and pepper. Pour the marinade over the chicken, seal the bag, and massage to coat evenly. Refrigerate for 20 to 30 minutes. Avoid marinating longer than 1 hour, as the lemon juice can begin to "cook" the chicken.
Preheat the grill to medium heat (400°F). Remove the chicken from the marinade and discard any remaining marinade. Clean and oil the grill grates. (I soak a rolled-up paper towel in vegetable oil, grab it with tongs, and rub it over the grates.)
Place the chicken on the grill. Grill the chicken for 4 to 5 minutes per side, or until it reaches 160°F. (Carryover heat will bring it up to the safe temperature of 165°F.)
Serve with grilled pita, Greek salad, tzatziki, and lemon wedges if desired.
Notes
Note 1: To grill pita: lightly brush both sides with olive oil. Grill for 30 seconds to 1 minute per side, until warmed and lightly toasted.Storage: Store leftover chicken in an airtight container in the fridge for 3 to 4 days. Freeze in a sealed freezer-safe bag or container for up to 3 months. Thaw overnight in the fridge before reheating.