Former President Bill Clinton instructed US politicians not to meet Mr Chen last time he passed through the US.
Beijing considers Taiwan a renegade province and regularly puts pressure on countries that offer to let Taiwanese leaders visit.
Mr Chen's stopover in the US on his way to Latin America is not an official visit, but it will have many of the trappings - including a stop at the New York Stock Exchange and a baseball game with an important Congressman.
Before his departure, Mr Chen called for more such visits.
"Taiwan is a sovereign, independent country," he said. "To let the international community acknowledge that, we must stand up and go out frequently."
The visit comes during a time of high tension between Washington and Beijing over issues such as US arms sales to Taiwan and surveillance flights near the Chinese coast.
Chen's troubles
Washington does not have official diplomatic relations with Taipei, and Taiwanese politicians need special permission for transit through the US.
Former President Bill Clinton instructed US politicians not to meet Mr Chen last time he passed through the US.
But the Bush administration has good relations with Mr Chen, and the visit will include the first ever visit by a Taiwanese president to New York, where he will meet about 20 congressman and New York Mayor Rudolf Giuliani.
There have been reports that Mr Giuliani will present Mr Chen with the key to the city and that the Taiwanese leader will visit the Metropolitan Museum of Art.
Republican Congressman Tom DeLay is to take the Taiwanese leader to a baseball game in Houston on his return trip through the US in June.
Dr Joseph Wu, deputy director of the Institute of International Relations in Taiwan, told the BBC: "Mr Chen is facing a lot of difficulties at home and is doing this to boost his popularity.
"When he returns to Taiwan he will declare victory."
'Whatever it takes'
New York has a large Chinese-speaking population and strong Chinese-language media presence, meaning Mr Chen's time there will be closely scrutinised.
Last month, Mr Bush appeared to remove a long-standing ambiguity in US policy when he said Washington would do "whatever it takes" to protect Taiwan in the event of a Chinese attack.
Previous presidents had carefully avoiding specifying how far the US might go for Taipei in such a situation.
Mr Bush later denied that his comments marked any change in US policy.