Need to fly to New York for business.

Booked me on a flight from SLC to ORD on United, which is scheduled to land in Chicago at 1 pm. Then booked me on a 2 pm flight from Chicago to New York on Delta.

Since it's a week long trip, l'd like to check a bag. Based on what I understand from United's most recent checked bag policy, I will have to collect my bag at baggage claim in Chicago, re-check it on Delta, then go back through security and on to my departure gate. All in an hour. At O'Hare. Seems virtually impossible.

Am I missing something?