Preheat the oven to 375 degrees F.
Combine the sour cream, blue cheese, hot sauce, milk and cream cheese in a food processor and process until smooth. Transfer the mixture to a medium bowl and stir in the chicken.
Scoop the chicken mixture into an 8-inch square baking dish and smooth the top. Bake until the mixture is warmed through and barely beginning to brown at the edges, 25 to 30 minutes. Transfer the dip to a rack and let cool for 5 minutes.
Scatter the carrots and celery over the top, then sprinkle with the parsley. Serve warm with tortilla chips, celery and carrots for dipping.
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