Place all the ingredients except chicken in the bowl of a small food processor, and process until a smooth paste forms. Rub the paste onto the chicken pieces, and marinate for 30 minutes in the refrigerator.
Preheat grill. Arrange the chicken pieces on the grill. Cook. Set aside.
To make tzatziki dip:
In a large bowl, combine all ingredients. Season with salt and ground black pepper.
Serve chicken bites with tzatziki sauce.
Notes
You can also thread chicken onto skewers to make kebabs.