I'm not familiar with O'Hare, but I would guess it's the domestic terminal, since your first flight is a domestic flight.
I agree with Lisa's advice, though. Pack all essentials in your carry on, as an hour connection at JFK for an international flight seems tight to me. I live in NJ, so I fly in and out of Newark regularly, which is always busy.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)