Raheem Sterling put the London side ahead in the 48th minute latching on to a low cross from Mason Mount and sending a curler beyond the diving Philipp Kohn into the left corner of his net.
But Noah Okafor equalised in the 75th minute with a low shot after Cesar Azpilicueta and Thiago Silva had failed to clear the ball. The Austrian side also drew against AC Milan last week.
It was a disappointing first game for new Chelsea coach Graham Potter, who took over at the end of last week, following the shock dismissal of Thomas Tuchel after Chelsea lost their first group game to Dinamo Zagreb.
Now Chelsea will have to face group leader Milan with a loss or draw could be the signal that they would not qualify from the group.