The International Olympic Committee (IOC) disqualified her for testing positive for steroid use.
"The Russian Federation team is disqualified from the women’s 4x100m relay. The corresponding medals and diplomas are withdrawn and shall be returned," the IOC said.
Her relay team mates in that competition were Aleksandra Fedoriva, Yulia Gushchina and Yevgeniya Polyakova.
Belgium finished second in the race and Nigeria won bronze.
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The IOC requested the world athletics federation (IAAF) to modify the results of the event and to consider any further action.
Chermoshanskaya, who finished eighth in the individual 200m in Beijing, tested positive for several anabolic steroids, including stanozolol, an anabolic steroid favoured by athletes and bodybuilders attempting to lose fat while retaining lean body mass.
Some users also say it reduces the amount of recovery time needed after injury.
The IOC stores samples for a decade to test with newer methods or for new substances. The ruling body conducted targeted retests before the Rio Olympics.
A total of 98 samples were positive in reanalysis of samples from both the Beijing Games and the 2012 London Olympics.
The re-tests were conducted ahead of the Rio Olympics as the IOC sought to root out potential cheats ahead of the Games.
Russia's track and field team, with the exception of one athlete based in the United States, was banned from the Rio Games over what the World Anti-Doping Agency said was a state-backed doping programme.
(Editing by Bill Rigby and Ed Osmond)
