The timing of Chen's death is unfortunate for the authorities. Almost exactly six years ago it was the death and subsequent state funeral of the former party chief, Hu Yaobang, that set the scene for the ill-fated student pro-democracy movement in Tiananmen Square.
Even before Chen's death on Monday, security in Peking had been stepped up in the seasonal clampdown ahead of the 4 June anniversary. Since the June 1989 massacre, the authorities have been extremely sensitive to the potential symbolism of funerals and graveyards.
Yesterday, the foreign ministry spokesman announced that "in accordance with the relevant regulations and [Chen Yun's] personal will, there will be no memorial meeting or ceremony to pay last respects".
As the authorities tread a fine line between political discretion and a lack of respect for such an eminent figure, it appears that there will be no large ceremony. Senior officials will say their farewells on the day of the cremation as they have for other deceased leaders since 1989. The date has not yet been announced, but flags will be flying at half mast.
Previously, state television has shown senior leaders paying their last respects to dead colleagues. It is not clear if that will happen this year because missing from the line-up would be the 90-year-old patriarch, Deng Xiaoping, whose health is too frail for public exhibition.
Chen was second only to Mr Deng in the hierarchy of party elders but in recent years had become the figurehead for hardline opposition to Mr Deng's fast-paced economic reform.
The Chinese government may want to use Chen's death as a practice run and to set a precedent for when Mr Deng dies. However, it is difficult to see how the authorities could avoid some public ceremony to mark Mr Deng's death, given his role as the architect of China's reforms.
In 1990, in an attempt to prevent dissidents using funerals to commemorate the Tiananmen Square dead, a regulation was passed banning "memorial meetings and ceremonies of last respects" for dead officials.