For the chicken: In a large pot, add chicken, onions, and celery and enough water to cover. Bring to a boil, and reduce heat to a gentle simmer. Skim off any foam, as necessary. Cook until meat is tender, 30 to 45 minutes. Remove thighs from the liquid and cool until able to touch. Shred chicken, discarding bones for another use (I add it back to the liquid to make stock), and set aside.
For the dip: Preheat oven to 350 degrees F. Add the cooked chicken, cream cheese, shredded cheeses, ranch dressing powder, and hot sauce in the bowl of a stand mixer fitted with the beater blade (this can also be done by hand) and mix on low until combined. Spread into a medium baking dish and cook until warm and bubbly, 25 to 30 minutes. Serve with corn chips, such as Fritos, and celery sticks.