Rinse the cucumber and the two tomatoes and cut them into large chunks. Peel the half red onion and slice it into thin half rings. Put the cut vegetables together with the handful of olives into a large mixing bowl. Season the chicken breast on both sides with salt and pepper.
Heat a small portion of the olive oil in a frying pan over medium-high heat. Fry the chicken breast for approximately ten to twelve minutes on both sides until golden brown and completely cooked through. Remove the chicken from the pan, let the meat rest briefly on a cutting board, and then slice it into strips.
Crumble the feta with your hands over the mixing bowl with vegetables and olives. Pour the remaining olive oil over it and add the oregano. Season the salad further with salt and pepper and toss everything well so the oil and herbs are distributed over the vegetables.
Divide the mixed salad among the plates. Lay the warm strips of fried chicken breast on top of the vegetables and serve the dish immediately.