1. Put the yogurt in a strainer lined with cheesecloth, a coffee filter, or a paper towel and set it over a bowl. Let drain in the refrigerator for 15 minutes. In a medium glass or stainless-steel bowl, combine the cucumber with 1 teaspoon of the salt; let sit for about 15 minutes. Squeeze the cucumber to remove the liquid. Put the cucumber back in the bowl and stir in the drained yogurt, the garlic, 1/8 teaspoon of pepper, and the dill.
2. Light the grill or heat the broiler. In a small glass or stainless-steel bowl, combine the oil, lemon juice, oregano, the remaining 1/4 teaspoon of salt, and 1/4 teaspoon of pepper. Toss the chicken cubes in the oil mixture and thread them onto skewers. Grill the chicken over high heat or broil, turning once, until done, about 5 minutes in all. Transfer the chicken to a plate.
3. Spread both sides of the pitas with the butter and grill or broil, turning once, until golden, about 4 minutes in all. Cut into quarters.
4. To serve, put the pitas on plates and top with the onion, tomatoes, and chicken skewers with any accumulated juices. Serve with the tzatziki and olives.
Wine Recommendation: This traditional Greek preparation goes with a number of choices to suit the occasion and your taste. Look for a very fruity red such as a Beaujolais, a sparkling wine from California, or a sauvignon blanc from northern Italy.