Combine ingredients in a plastic food storage bag. Marinate chicken for at least 4 hours and up to 6.
For the chimichurri, combine parsley, mint, Fresno, shallot, garlic, sherry, honey and lemon in a food processor. Stream in olive oil while machine is running until combined. Season with salt and pepper, and reserve.
Remove chicken from marinade and thread onto skewers. Season with salt and pepper
On a grill or broiler, grill skewers for 3-4 minutes on each side until completely cooked through. Serve on top of pitas with sauce alongside.