The Hoops have dominated Scottish football in recent times and no other team has won a trophy since 2016.
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While they have played three games fewer, Celtic are well behind league leaders Rangers who are 16 points clear at the top. Hearts, who are top of the second tier, had hopes of an upset.
It went to penalties and it was Celtic who blinked first when Christie saw his effort saved by ex-Hoops goalkeeper Craig Gordon.
However, Hearts failed to capitalise as they missed their next two spot kicks and Kristoffer Ajer stepped up to seal the win 4-3 on penalties.