Place chicken breasts in a medium pot and cover with chicken broth. Bring to a light boil, then reduce heat to low and simmer for 12-15 minutes until the internal temperature reaches 165°F (74°C).
Remove chicken from the pot and transfer to a cutting board. Allow to cool for 5 minutes, then shred using two forks or dice into 1/2-inch cubes.
In a small mixing bowl, prepare the ranch dressing by whisking together the avocado oil mayonnaise, lemon juice, apple cider vinegar, garlic powder, onion powder, sea salt, and black pepper until smooth.
In a large mixing bowl, combine the shredded chicken, diced celery, red onion, parsley, dill, and chives.
Pour the dairy-free ranch dressing over the chicken mixture and toss thoroughly to ensure even coating.
Taste and adjust seasoning with additional salt or pepper if desired.
Cover and refrigerate for at least 30 minutes to allow the fresh herb flavors to fully meld before serving.
Serve chilled over a bed of greens, inside lettuce wraps, or as part of a meal prep container.