Chen was escorted to the tightly guarded Hengshan command center in the capital around 8:00 pm Wednesday, 10 minutes after the beginning of the drill codenamed "Yushan No 2", the United Daily News said.
Other top government officials joining the 150-minute drill included Premier Su Tseng-chang, Defense Minister Lee Jye, National Security Council secretary-general Chiou I-jen and Mainland Affairs Council chairwoman Tsai Ying-wen, it said.
Television footage showed limousines carrying officials rushing to the command center.
The scenario was that "the Chinese communist troops launched a surprise assault on the presidential building, pitting the president against a dangerous situation," the paper said.
The exercise aimed to review the emergency capabilities of government units, it said. The defense ministry declined to comment on the report.
Taiwan held the first such exercise last year, without the participation of the head of state.
A Pentagon report has warned that China is building up its military at a pace that is tipping the balance against Taiwan and could pose a credible threat to other armies in the region.
China regards Taiwan as part of its territory and has vowed to invade should it declare formal independence.