Combine the shredded chicken and diced red onion in a large mixing bowl.
In a separate small bowl, mash half of the avocado cubes with the lime juice, olive oil, minced garlic, salt, and pepper until relatively smooth.
Transfer the avocado mash into the large bowl with the chicken and onion.
Add the remaining cubed avocado and chopped cilantro to the bowl.
Gently fold all ingredients together using a rubber spatula until the chicken is evenly coated, taking care not to completely mash the remaining avocado chunks.
Serve immediately or refrigerate in an airtight container for up to 2 hours.