Preheat the grill to medium and lightly brush the grate with oil.
Combine the apricots and orange juice in a small, microwave-safe bowl. Microwave until the apricots are soft, about 3 minutes. Set aside.
Whisk together the lemon juice, vinegar, oregano, garlic, 1/4 teaspoon salt and some pepper. Slowly drizzle in the olive oil while whisking. Sprinkle the chicken breasts all over with 1/4 teaspoon salt and some pepper, then toss with 2 tablespoons of the dressing. Grill the chicken until nicely marked and it reaches an internal temperature of 165 degrees F, 4 to 5 minutes per side. Let rest for a few minutes, then slice.
Brush the pitas with some of the remaining dressing and grill lightly on each side. Cut each into six triangles. Combine the lettuce, tomatoes, pepperoncini and cucumbers with the remaining dressing. Divide the chicken, pita and salad evenly among four plates.
For dessert, divide the yogurt among four small bowls and top with the apricots and juices, serve.