Preheat the oven to 350°F. Blind bake the pie crust for 9 minutes. Remove it from the oven, it's okay if it cools down while you finish prepping. You can fill it while it's hot or cool.
Whip the cream cheese until it's smooth. It'll mix much easier when it's at room temperature. Add the eggs, cream, Cajun seasoning, salt, pepper, tomatoes, and green chiles and stir. Add the chicken and cheese. Stir to combine.
Pour the mixture into the pie crust.
Bake for 25 to 30 minutes or until set in the center. Remove from the oven and cool for 5 minutes before serving. Serve. Store any leftovers in the refrigerator in an airtight container for 3 days.