Heat oven to 200° F. Wrap the bread in foil and place in oven.
In a medium bowl, combine the tomatoes, onion, Feta, and olives.
In a large bowl, combine the oregano, thyme, pepper, 1 ½ teaspoons of the vinegar, and the lemon juice. Slowly add 4 tablespoons of the oil, whisking constantly until incorporated.
Pour 2 ½ tablespoons of the vinaigrette over the tomato mixture, toss, and set aside. Add the chicken to the remaining vinaigrette, toss, and set aside.
Heat the remaining oil in a large skillet over medium-high heat. Transfer the chicken (without the liquid) to the skillet and heat, turning occasionally, until cooked through, about 5 minutes.
Meanwhile, in a small bowl, combine the yogurt, cucumber, dill, and the remaining vinegar. Spread the bread with the yogurt sauce and top with chicken and tomato salad. Fold in half, if desired.