Chop and shred the chicken into a large bowl.
Cut the avocados in half and remove the seeds. Scoop the flesh from one of the avocado halves and add it to the bowl with the chicken. Squeeze a little lime juice over the surface of the 3 remaining avocados to prevent browning.
Add the mayo to the bowl if using, along with the rest of the lime juice, the garlic, shallot, parsley or cilantro, and the minced cucumber. Toss to combine as you mash the avocado with a fork until everything is smooth.
Scoop out the chicken mixture and place it into the hole area where the seed was in the 3 avocado halves. Garnish with the cucumber slices and extra parsley or cilantro. Serve.