Add chicken to the grill and grill each side for 5-6 minutes, until there is no more pink. For the last minute, add 1 slice of mozzarella to the top of each chicken. Close the grill and let the cheese slightly melt. Remove from grill and let sit.
Next add ciabatta bread to the grill, place the inside part of the bun on the grill and toast for 1-2 minutes until slightly charred. Remove.
Assemble the sandwich: spread 1½ tablespoons of pesto on the bottom bun, place the grilled chicken and melted cheese on top of the bottom bun, then a slice of tomato, and a few slices of fresh avocado, add the top bun. Serve!