The 34-year-old, who was crowned Olympic champion at London 2012, was found to have taken the steroid turinabol when she came third in Beijing behind Belgium's Tia Hellebaut and Blanka Vlasic of Croatia, the International Olympic Committee said in a statement.
It did not say who will now get the Russian's bronze, but another Russian, Yelena Slesarenko, came fourth.
The IOC is reanalysing stored samples from athletes of the Beijing and London Games as part of efforts to clean up athletics and Chicherova is just the latest to be snared.
The Russian track and field team were barred from the Rio Olympics in August because of state-sponsored doping.
In June, following a decision by world athletics' governing body the IAAF to uphold the ban on Russian athletes, Chicherova told AFP: "This measure is too harsh for those who were never involved in doping scandals. It's unfortunate to be a witness to such fate-changing decisions."
A month later she said she had been banned by the IAAF for failing a drug test in relation to 2008.
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