Put the vinegar and garlic in a food processor and pulse until the garlic is chopped into small pieces. Add the Dijon and blend it in thoroughly. Turn the food processor on again and slowly drizzle in the olive oil until the dressing thickens.
Put the yoghurt and dill in a mixing bowl, add the dressing and whisk together until combined.
for the pitas:
Heat the oven to 450, then throw the pita bread in to soften.
Take 4 squares of aluminum foil and fold one of the corners in about 4 inches.
Place one piece of pita on each foil sheet, with the top part of the bread sticking up over the fold about 1 inch.
Divide and stack the romaine, chicken breasts, tomatoes, cucumbers, olives and feta onto each piece of pita. Finish with a liberal amount of the tzatziki on top.
Pull the pita together with your fingers, then use your other hand to pull up the foil and pinch and seal it together, to hold the sandwich in form.