Taiwan debate on ousting leader
The opposition parties are urging the president to step down, saying he has lost the public's confidence.
It follows a series of corruption scandals in recent months allegedly involving his family and aides.
Lawmakers from Mr Chen's governing Democratic Progressive Party and its main parliamentary ally, the Taiwan Solidarity Union, left the talks.
It was a day of drama as Taiwan's legislature started a process that could force the president out of office.
When lawmakers from the DPP and the TSU walked out of the session, they said they would stay away until the motion was voted on next week.
Some held a short protest chanting and holding banners, saying moves to unseat the president were harming Taiwan and causing social turmoil.
But in a live evening television broadcast Ma Ying-Jeou, chairman of the main opposition party, the Nationalists (or Kuomintang), urged the president to resign voluntarily.
He said the longer Mr Chen stayed in office the more harmful it was for Taiwan.
He also said the president's two-hour speech broadcast the previous night, in which he had denied opposition charges that he was unfit to govern, had failed to clearly answer many of the allegations.
The political fireworks are likely to continue for some time.
Many analysts believe the parliamentary vote to remove the president from office will fail, but if it does the opposition parties say they will start to push for a vote of no confidence in the cabinet.