Marinate (10 min): Mix oil, lemon, zest, oregano, garlic, salt, and pepper. Toss in chicken; rest 10 minutes.
Cook Chicken: Grill or skillet over medium-high, 4–6 min per side to 74°C/165°F. Rest 5 minutes; slice.
Make Dressing: Whisk all dressing ingredients until glossy.
Toss Salad: In a large bowl, add cucumber, tomatoes, red onion, olives, feta (and romaine if using). Pour in most of the dressing; toss gently.
Finish & Serve: Top with warm sliced chicken, herbs, and the remaining dressing. Serve with lemon wedges (and warm pita/tzatziki if you like).