In a large bowl, whisk together all the ingredients for the marinade and set it aside. Cut the chicken breasts into cubes and add them to the bowl. Thoroughly coat the chicken pieces with the marinade.
Place the marinated chicken pieces into a large gallon sized storage bag and place in the fridge for at least 3 hours, or overnight.
Preheat your oven to 450 degrees F and line a broiler safe rimmed baking sheet with aluminum foil. Thread the chicken pieces with your choice of onions, vegetables, peppers, etc. Place the completed skewers on the baking sheets and bake for 15 minutes.
Then switch your oven to high broil. Please the baking sheets underneath the broiler and continue to cook until the chicken is nicely browned, about 5 minutes
Carefully remove the chicken and vegetables from the skewers and serve with your homemade tzatziki sauce.