Buffalo Chicken Dip

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1 cup sour cream

1/2 cup finely crumbled blue cheese (about 2 1/2 ounces)

1/2 cup mild hot sauce, such as Frank's

1/4 cup whole milk

Two 8-ounce packages cream cheese, at room temperature

2 cups chopped cooked chicken (from about 1/2 rotisserie chicken)

1 medium carrot, finely chopped (about 1/2 cup), plus carrot sticks, for serving

2 stalks celery, finely chopped (about 1/2 cup), plus celery sticks, for serving

1 tablespoon finely chopped flat-leaf parsley

Tortilla chips, for serving