The decision was read out to stunned silence at Liverpool's Echo Arena as the home favourite was left disappointed.
One judge had Chilemba winning by four rounds with a score of 116-112, while another had Bellew by one point and the final man at ringside could not split them.
In a clash of styles neither man was able to land cleanly very often, with defence the name of the game.
Bellew comfortably won the opening few rounds with his opponent offering little in attack, even if he was hard to hit.
Around the midway stage, though, the balance shifted and Chilemba began to believe that he could win it, catching Bellew with a couple of clean right hands.
In round eight the away fighter really caught the eye with his work rate and speed, but never hurt Bellew.
The final few rounds were close as both men sensed that the job was not done. Chilemba made Bellew miss but rarely hit the Liverpudlian, who thought that he had done more than enough to win the fight.
The winner would have been due a shot at the WBC title but the two men may have to do it all over again after this stalemate.