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Flying from Chicago to JFK, and then to Italy, you don't need to go through security again. Only when you are coming from Italy.
Delta is on terminal 3, but terminal 3 have 2 different zones, so It depends which gates you're arriving, and which one is for your departure.
So, I think 50 mins can be enough, if planes are on time. Maybe ask the hostess to a little more help: I know they have small electrical car to go from one side of the gate to the other, so maybe they can provide you one, if your gates are far away.
Hope this can help.