Chicago-style pizza in NYC for inauguration office party; delivery to midtown
You might have to go with the chain Pizzeria Uno. Not as good as Lou Malnatis, Ginos, etc (I'm a native Chicagoan) but it should do.
here are the NYC locations: http://www.unos.com/location.html
Another idea is that Lou Malnatis will ship pizzas (packed in dry ice) that you can cook yourself: http://www.tastesofchicago.com/catego...
I'm not certain why the moderators deleted my response since it didn't contain vulgarity or go off-topic, but let me try to post the helpful information.
There is no Chicago-style pizza in NYC. Yes there's Pizzeria Uno, but if you've never had deep dish before, Uno shouldn't be your first experience. The proliferation of Uno is exactly why New Yorkers hate Chicago-style pizza. You can order terrific frozen pizza from Lou Malnati's or Gino's, but you will need to have enough oven space to make the pizzas.
If you are gung-ho on serving Chicago foods, you could conceivably order 40 Chicago-style hot dogs from Shake Shack, because other than that, most foodstuffs Chicagoans take for granted, from pizza to giardiniera, are unavailable in New York.