1) In a non-reactive dish, combine the lemon juice, olive oil, oregano, salt, and pepper and mix together. Add the chicken breasts to the dish and rub both sides in the mixture. Cover the dish with cling film and let marinate in the refrigerator for at least 30 minutes and up to 4 hours.
2) Combine all the ingredients for the dressing in a resealable container and shake vigorously. Refrigerate until ready to serve, and then bring to room temperature before tossing salad.
3) Cut off any dark tips and the bitter white bottoms from the cos lettuce leaves. Cut the lettuce into 2.5-cm strips and place in a bowl that is large enough to hold all the salad ingredients comfortably. Scatter cucumber, tomatoes, red onion, olives, and feta over the top. You can prepare the salad up to a few hours in advance. Cover it with moist kitchen paper and refrigerate until 30 minutes before serving.
4) Heat a nonstick skillet or griddle pan over high heat. Add the chicken breasts and cook, turning once, until well browned, about 4 to 5 minutes on each side or until cooked through. Let the chicken rest on a cutting board for a few minutes before slicing it into thin strips.
5) Give the dressing a good shake and pour it into a nice serving bowl, using the lid to sieve out the garlic.
6) Toss salad just before serving and fan chicken out on top.