Cut the chicken breasts into thin strips. Mix together the polenta, onion powder, paprika, cumin seeds and pepper in a plastic bag. Add the chicken strips, a few at a time, and toss well to coat all over. Remove, shaking off the excess, and set aside on a plate while making the sauce.
To make the sauce, squeeze the grated cucumber, in handfuls, to remove excess moisture, then put into a bowl. Add the remaining ingredients and stir to mix. Set aside.
Preheat the grill to high. Heat a ridged griddle or heavy frying pan and add half the oil, swirling it around the pan until lightly coated. Add half the chicken strips and cook over high heat for 2–3 minutes or until golden brown all over and cooked through, turning once. Keep hot while cooking the remaining chicken strips, using the rest of the oil.
Meanwhile, warm the pitta breads under the grill for 1 minute on each side. Split down the side of each pitta to make a pocket.
Fill the pitta pockets with the salad leaves. Pile in the chicken strips, spoon over the sauce and serve.
Some more ideas
Middle Eastern chicken sandwich: Put the chicken breasts between sheets of very thin plastic and pound with a belna to a thickness of about 1cm (½in) all over. Lightly beat 1 egg and pour on to a plate. Put 100g fine fresh white breadcrumbs on another plate. Season each chicken breast with pepper, then dip into the egg and coat both sides in breadcrumbs, patting them on lightly. Heat half the oil in a ridged griddle or frying pan and cook the chicken breasts, two at a time, for 6 minutes or until golden, turning once. Finely shred ½ small head each of white and red cabbage, and thinly slice 1 sweet white onion. Toss with 2 tbsp chopped parsley and 2 tbsp lemon juice. Spoon 1 tbsp hummus into each warmed pitta pocket, add some cabbage salad and fill with the hot chicken breasts.