Preheat oven to 400ºF.
In a shallow baking pan, whisk together lemon juice, soy sauce, honey, minced garlic, oil and oregano; add chicken and turn to coat.
Bake until chicken is cooked through, about 25 to 30 minutes, spooning sauce over chicken once or twice during cooking.
Meanwhile, in a small bowl, combine yogurt, cucumber, dill and garlic powder.
When chicken is cool enough to handle, slice each piece crosswise into thin strips and place inside pita pocket halves. Spoon 2 tablespoons of yogurt sauce into each pita half. Yields 2 halves per serving.