The fastest service was Wuhan–Guangzhou, which averaged 313 km/h on non-stops, but is not run any more.
Chicago-NYC with stops would probably be 5 hours, which is barely competitive with flying. The intermediate stops would potentially make it viable though.
I would take a 5-hour train from NYC to Chicago over flying, because of the extra comfort and because getting to/from the airport on either end is a hassle.
However, modern high-speed rail lines are capable of 350 km/h top speeds, and there are lines that average 300 km/h, with stops included (e.g., Beijing-Nanjing).
5 hours, from New York Penn station to Chicago Union Station (as opposed to killing an hour to JFK/LGA/EWR and another hour from O'Hare), without having to be an hour early on top of that so the TSA can fondle you, sitting in a normal sized chair, allowed to stand up whenever you want, and complimentary wifi the whole time. Yeah, that's competitive with flying.
Chicago-NYC with stops would probably be 5 hours, which is barely competitive with flying. The intermediate stops would potentially make it viable though.