Place the first 8 ingredients in a medium bowl and toss to coat the chicken. Cover, refrigerate and marinate 2 hours.
Preheat barbecue or indoor grill to medium-high. Thread one piece of chicken on each skewer. Lightly oil the bars of the grill. Season the chicken with salt. Grill 2 to 3 minutes per side, or until cooked through.
Note: Chicken breast fillets are tender strips of meat removed from the breast and sold separately in our Meat Department.
Recipe Options: Make Greek-style pork or lamb skewers by replacing the chicken with 16 thin strips of the pork leg or lamb sirloin. If you would like to make you own tzatziki sauce to serve with the skewers, start by setting a large sieve over a bowl. Coarsely grate half an English cucumber into the sieve. Press on the cucumber and squeeze out as much liquid as you can. Discard the liquid. Add to the cucumbers 1 1/4 cups of thick, Greek-style yogurt, 2 Tbsp. chopped fresh mint, 1 chopped garlic clove, 1/2 tsp. finely grated lemon zest, and 1 Tbsp. lemon juice. Mix to combine and season with salt and white pepper. Cover and refrigerate until needed.