Step 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.

Step 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.

Step 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.

Step 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.