You need to check air carriers policys on transporting a weapon. I have numerous times flown into and out of O'Hare with a gun. In general you need to have the gun empty and I leave it open in a locked case in my luggage. You cannot have any ammo with the weapon or in your bag.
You need to declare at the check in counter you have a gun in a case locked. Heres a tip if theres a long line grab a Sky cap and tell him you need to declare a gun and everytime I get moved to the front or taken to another area for check in. Also O'Hare is real hinky about guns.The last time I had to show my weapon to 3 supervisors then follow the supervisor to the xray machine and visually verify the bag went through the conveyor. Now its just the opposite for me leaving NM to chicago. Here I just show it once and get going. As for traveling through the state you need the gun secured and in the farthest most rear of the car.Also empty and best broken down.
When I'm in that state I dont open the case till I get to where I'm shooting or in my residence of the time. I have transported over a dozen times this way. My niece is an avid shooter and we enjoy shooting together.