Place your chicken on a large cutting board and cut it in half horizontally to butterfly it. Place a piece of plastic wrap over the chicken, and pound it until it is very thin with a meat mallet.
Marinate chicken in a few tablespoons of olive oil, a generous amount of salt and pepper, the juice of 1 lemon, and some fresh, roughly chopped herbs. Set aside while you compose the rest of the salad.
In a large bowl, combine all of the other salad ingredients and toss lightly with your hands.
In a stovetop grill pan, grill chicken in 2 batches until done and nicely charred with grill marks. On a clean cutting board, slice chicken in diagonal slices.
Drizzle some lemon juice and a little extra virgin olive oil over the salad, and season with a little salt and pepper. Toss well. Top salad with sliced chicken and more fresh herbs, and serve.