Madrid Airport Transfer Time

I'm assuming you are flying Iberia IB6274 (AA codeshare) from ORD to MAD. That's the only non stop ORD-MAD. You'll be arriving to Terminal 4-S (Satellite) which is a separate terminal in the middle of the tarmac. Your Granada flight, operated by Air Nostrum, a subsidiary of Iberia, will depart from Terminal 4.
Terminal 4-S is connected to Terminal 4 via an underground people mover which goes under the runway 36/L. One hour is a short time, considering you have to go through passport control first. Also the flight from Chicago might be late (for example today it arrived 2 and 1/2 hours late). However I would book it anyway If you don't make your connection, Iberia will put you on the very next flight to Granada, there are five a day going to Granada, if you miss the first, you have 4 more tries to go.

Roberto - thanks for your help. That is pretty much what I thought, but here is my dilemma. I am headed there to visit my daughter who will be studying in Granada for the semester. Our original plan was to grab a bus to Cordoba that afternoon until I noticed the short connection time. Perhaps I am better off booking the next later connecting flight which would give me four hours in Madrid? Then I would be less likely to miss the connection and have to worry about other flights being full, since it will be holy week... From Cordoba we plan to make a loop to Sevilla, Ronda and back to Granada. I know there are alot of busses from Granada to Cordoba, but since it will be during holy week, I would feel better if we had tickets in advance. We have to end our trip in Granada as she will be sending an extra suitcase full of winter things home with me as she pares her belongings down in preparation for traveling over the summer. This new plan would give me four hours in Madrid and i would arrive in Granada at 1:10. Then do you think we could catch the 3:00 or the 4:30 bus to Cordoba without difficulty? Thanks again for your help!

One hour is a short connection on a domestic flight, even more so on an international flight. That said, if the flight is timely you can make it. If it's one hour late, you won't. Nobody can guarantee you anything. I have sometimes arrived in Europe 5 hours late for a reason or another and missed my connections. It's rare but it happens. Nobody can't even guarantee you that your later MAD-GRX flight will arrive on time for you to catch the 15:00 hours bus. If it's timely, and most of the time it will be, you should make it, but who knows. You could also consider postponing your trip to Cordoba by a couple of days, so that you don't have to rush on your day of arrival when you are tired for the long flight and the jet lag. Remember that your flight from ORD arrives at MAD at 7:40 (that is 00:40 in Chicago). By the time you reach Granada with the later flight, it will be 13:10 (or 6:10 am in Chicago), then your bus leaves at 15:00, or 8:00 am in Chicago. Basically you'll be doing all this travel from Madrid to Granada while your biological clock is on nighttime Chicago. After all of that you want to get on a bus for another 3 hours. That's too much for me. That's way over 24 non stop traveling from the time you left Milwaukee. Besides, if you want to go to Cordoba first, why do you need to fly to Granada and all of that. Just fly to Madrid and take a bullet train to Cordoba. You'll be there in less than 2 hours from Madrid. I would take it easy the day of arrival and stay in Granada for 2 nights. If you catch the first flight you can take a stroll in El Albaicin district, have dinner and rest. The day after your arrival you could visit the Alhambra after a good night sleep. Then the morning after your second night in Granada, you could take your trip to the rest of Andalucia.

I lived in Malaga for years and my mum would fly over from the states to visit me. In all of her experiences her flight from TPA was usually late and if she had a short lay over she would either cut it too close or she would miss her connecting flight to Malaga. Its not worth the stress of hoping and praying that your original flight takes off on time and that you make the connecting in Madrid. I would say take the 4 hour lay over then you can take your time, get through customs and know that you will make your flight. Also Roberto is right I would consider taking it easy as the journey is a long one. I do recommend that you stay up all day once you arrive to Granda but I think that it will be a push to be on your A game after the long flight. I know everyone is different but my mom was always fine the first few hours of her arrival in Malaga (could have been adrenaline) but by mid day she was tired and she normally had to fight to stay up til 5 or 6 pm and it wasnt easy. They always say it takes one day for each time zone but my mom was normally fine by her 3rd day!!!!