Heat the oven to 375°F. Shred the rotisserie chicken into 3 cups, discarding the skin and bones.
In a large bowl, stir together the Greek yogurt, cream cheese, hot sauce, 1/4 cup of the cheddar, the blue cheese, and half of the green onions until smooth.
Fold in the chicken until evenly coated.
Spread the mixture in an 8-inch square baking dish and sprinkle with the remaining 1/4 cup cheddar.
Bake 20 minutes, until bubbling at the edges.
Turn off the oven and let the dip stand 5 minutes. Scatter the remaining green onions on top and serve warm with the celery and carrot sticks.