Hu arrived in Chicago Thursday following a summit with President Obama and talks with congressional leaders in Washington.
Hu visited Walter Payton Prep on the city's Near North Side where students are involved in an intensive Chinese cultural program.
"We are especially struck by how bright and inquisitive the students are by your many talents and your all-around development," the Chicago Tribune quoted Hu as saying after two dozen students in the school's Chinese language program greeted him in his native language. "We have decided to invite 20 members of the faculty and students of this school to visit China in the summer holidays."
Students also presented him with a bouquet of orchids and performed a capella.
"For Chicago students, learning Chinese is about more than learning a language. It's a life-changing experience," Mayor Richard Daley, Hu's host in Chicago, told the students. "This should be a day for all of you to remember for the rest of your lives -- the day the leader of a nation came to your school."
Hu and Daley were scheduled to visit an exhibition in Woodridge, Ill., showcasing a Chinese-owned auto parts plant and other companies, officials said.
Daley hosted a Thursday dinner for the president that was attended by Chicago political and business leaders.
"China wishes to work with the United States to fully tap our cooperation potential in fiscal, financial, energy, environmental, infrastructure development and other fields," Hu told the guests through an interpreter.
He also called for a "level playing field" for Chinese companies that want to invest in the United States and pressed for greater Chinese access to U.S. technology.
Daley, who said he intended to make Chicago "the most China-friendly city in the United States," called the Chinese leader a "man of vision," the Chicago Sun-Times reported.
"We want to establish a new partnership between Chicago and China that will benefit the future generations for years to come," the Chicago Tribune quoted Daley as saying.
About 300 Chicago-area companies have offices in China and 30 Chinese companies have Chicago operations, city economic-development officials said.