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 1/2 teaspoons of the vinegar, and the lemon juice. Slowly add 4 tablespoons of the oil in a steady stream, whisking constantly until incorporated. Pour 2 1/2 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 but not 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 some of the yogurt sauce and top with the chicken. Add the tomato salad and fold.
Tip: Greek souvlaki traditionally calls for lamb, but you can also make it with chicken breasts, turkey cutlets, or shrimp.