Cook the chicken breasts and shred them. Place the shredded chicken in a medium sized mixing bowl.
Put the basil, avocado, olive oil, sea salt, and pepper in a food processor and blend until smooth. Make sure to scrape the sides a couple of times to incorporate all the ingredients.
Pour the avocado and basil mixture into the mixing bowl with the shredded chicken and toss well to coat.
Keep in the refrigerator until ready to serve. Garnish with parsley