Wu has pleaded not guilty to the charges against her.
She was indicted on November 3 along with three former presidential aides on charges of skimming $450,000 from a special presidential fund set aside to sustain Taiwanese diplomatic activities abroad. The other aides also pleaded not guilty.
Prosecutors have said that Chen could face the same charges once he leaves office. He is protected with immunity until then.
Opposition legislators allege that Chen’s family and inner circle exploited their proximity to him for personal financial gain.
Chen has said that he and his wife are innocent and has promised to step down if Wu is found guilty.
Her attendance at Friday's proceedings was in doubt until the last minute because of her health, and the trial began with declining public support for her.
She was once widely respected for the suffering she endured.
She was run over by a truck in 1985, as her husband and allies from the incipient Democratic Progressive Party chipped away at the monopoly on power that Taiwan’s Nationalists held at the time.
Chen said the incident, which left Wu paralysed from the waist down, was an attempt on her life by the Nationalists - a charge they deny.
Public sympathy for her began to wane in 2005, when it was alleged that she had used insider information to make large sums of money on the stock market.
It was also alleged that she had been given expensive gift vouchers from an upscale Taipei department store in exchange for helping to facilitate a change in ownership.
Prosecutors found there was insufficient evidence to prosecute her with receipt of the vouchers, but she promised to suspend her stock trading activities following public outcry.
The media has also criticised her for her collection of jewellery, which includes an expensive Breguet watch and jade earrings worth $185,000.