Chimera beat Nikolai Khabibulin between the legs with a shot from the right circle to complete a 2-on-1 break.
Sergei Fedorov, Rostislav Klesla, Joe Motzko and Fredrik Modin scored in regulation for the Blue Jackets, who trailed 3-1 in the second period but rallied to take a 4-3 lead late in regulation.
Motzko's goal was his first in the NHL.
Bryan Smolinski had two goals for Chicago. His second, with 1:33 left in regulation, forced overtime. Patrick Sharp and Jim Vandermeer also scored in regulation for Chicago, which lost its seventh straight (0-6-1).