Chop the chicken and broccoli into small, bite-sized pieces. Finely dice the red onion.
In a bowl, stir together the pesto, mayonnaise, and lemon juice.
Add the chicken, broccoli, and red onion to a large bowl. Pour the creamy pesto over top, and add the freshly cracked pepper. Stir to combine.
Taste the salad and add salt or pepper to your liking. Serve immediately or refrigerate until ready to eat.
