Preheat the oven to 475°F (245°C) and arrange a rimmed baking sheet or shallow baking dish.
Spread the tortilla chips in an even layer on the prepared baking sheet or dish.
In a small saucepan, combine the Buffalo wing sauce and 1/2 cup water and bring to a simmer over medium heat.
Add the shredded cooked chicken to the simmering sauce and heat until warmed through, about 2–3 minutes.
Use a slotted spoon or a strainer to remove the chicken from the sauce, reserving the sauce for later.
Spread the sauced chicken evenly over the tortilla chips, then sprinkle the shredded cheddar cheese on top.
Bake in the upper third of the oven until the cheese is melted, about 5–7 minutes.
Remove the nachos from the oven and drizzle with blue cheese dressing, sprinkle blue cheese crumbles, and scatter the chopped celery over the top.
Finish by spooning the reserved wing sauce over the assembled nachos and serve immediately.
