Place chicken breasts between plastic wrap and gently pound to even 1-inch thickness for uniform cooking.
In a medium saucepan, combine 4 cups water, 1 tsp salt, 2 bay leaves, and 5 peppercorns for poaching liquid.
Bring liquid to 170°F (77°C), add chicken, reduce heat to maintain 165°F (74°C), and cook for 12-15 minutes until internal temperature reaches 165°F.
Transfer chicken to cutting board, rest for 10 minutes, then slice against the grain into ½-inch strips.
Whisk 1 tbsp olive oil, lemon juice, minced garlic, oregano, salt, and pepper. Fold in Greek yogurt for creaminess.
In a large bowl, combine mixed greens, cherry tomatoes, cucumber, red onion, and olives.
Add sliced chicken, drizzle with dressing, top with crumbled feta, and gently toss to combine.