Stir together the mayonnaise, pesto, lemon juice, and pepper in a bowl.
Rinse and drain the chickpeas. Roughly chop the parsley. Finely dice the red onions (soak the red onions in cold water for 5 minutes for a milder onion flavor). Add the chickpeas, parsley, and onion to a large bowl.
Pour the dressing over the chickpeas, parsley, and onion. Stir to combine. Serve as is or slightly mash the chickpeas for a thicker consistency. Serve immediately or refrigerate until ready to eat.