Prepare all of the ingredients.
Place the shredded cucumbers for the tzatziki sauce onto a paper towel, wrap it up and squeeze out as much liquid as you can. Place in a bowl and add remaining ingredients for the sauce. Mix until well combined and place in refrigerator until ready to serve.
In a large saute pan over medium high heat add oil. Sprinkle chicken with seasonings and then add to pan. Cook, stirring regularly for 8-10 minutes (until chicken is cooked through).
In a small bowl, combine the roasted red peppers, cucumbers, tomatoes, red onions, red wine vinegar and fresh dill.
Now to build the nachos: you can do this on large platter and serve it family style or you can make individual plates for everyone. Start with a bed of pita chips, layer with chicken, then the red pepper "salsa", followed by feta cheese crumbles and finally a sprinkle of fresh dill.