This flight arrived at ORD today at 4:50am to a grand welcome of numerous emergency vehicles. We were all wondering if it was all for us! Then the captain came on and confirmed that indeed it was and that earlier in the flight they shut off one of the engines as it had zero oil pressure. The landing was pretty uneventful but there was an unusual vibration when the engine was revving during approach. The pilot said that in 30 yrs of flying he had never yet lost an engine! The only really unusual thing was that one of the FAs at the front of E+ just barely made it to her seat before wheels touched and the other did not manage to buckle her seatbelt. They had been chatting and then doing landing things. Not sure if they knew of the issues...we were not told in advance and likely for the better.