Combine dressing and mayonnaise in a bowl; spoon into a large plastic ziploc bag.
Add chicken; seal bag and turn to coat.
Refrigerate for 20 minutes to 2 hours.
Remove the chicken from the bag, discarding marinade.
Thread chicken and onion alternately onto skewers.
Grill over medium-high heat, turning occasionally, for 8 to 10 minutes, until chicken is cooked through
If using wooden skewers be sure to soak them for at least 15 minutes before you put them on the grill.