He was greeted with a standing ovation, and was joined on stage by six students and recent college graduates for a discussion about the need for greater civic engagement among young people.
The 55-year-old Democrat, who ended his two terms at the White House in January -- handing power over to Donald Trump -- said he was "incredibly optimistic" about the future.
"I'm spending a lot of time thinking about: what is the most important thing I can do for my next job?" Obama said in his opening remarks at the university, where he once taught law.
"The single most important thing I can do is to help in any way I can to prepare the next generation of leadership to take up the baton and to take their own crack at changing the world," he said.
Obama took a few questions from the participants on stage, but mainly listened -- and did not offer any substantive commentary on how Trump is doing, in keeping with presidential protocol, which dictates that past residents of the White House do not step on the toes of the current occupant.
Until Monday, he had not given a public speech or an interview since leaving the White House on January 20.
He has tweeted a few times and issued a few statements through a spokesman, notably to defend his signature domestic policy achievement, health care reform -- which Trump's Republicans are now hoping to dismantle.
"I was glad that (Trump) didn't come up," said Raquel Navarro, 22, who was in the audience. "I was hoping to not talk about any of the ridiculousness that students feel is always taking over our news."
Obama's silence comes even as Trump lobbed accusations on everything from Syria, with the Republican all but accusing Obama of bearing responsibility for chemical weapons attacks by the Damascus regime, to gang violence in America.
Series of public events
Youth civic engagement and community organizing are at the heart of the mission of the Obama Center, which is to be located on Chicago's South Side, where Obama started his career as a community activist.
"That creation of empathy then promises a different kind of civic response and political response," Obama said.
The former president also injected humor into the discussion, as when he addressed the challenges of a younger generation whose everyday exploits are chronicled on social media.
"If you had pictures of everything I'd done when I was in high school, I probably wouldn't have been president of the United States," he joked.
"I would advise all of you to be a little more circumspect about your selfies and what you take pictures of. Just a suggestion."
Since leaving office, Obama has earned some social media interest in his vacations -- he went kitesurfing in the Caribbean with British billionaire Richard Branson and spent nearly a month in French Polynesia, vacationing on media mogul David Geffen's yacht and reportedly working on his book.
After Monday, his public schedule will pick up pace.
Next month, he will receive the 2017 Profile in Courage award from the John F. Kennedy Library Foundation in Boston and give a private paid speech in Italy.
He will also deliver a speech at a Protestant church gathering at the Brandenburg Gate in Berlin, with Chancellor Angela Merkel at his side.
"It kind of scared me that I might not be hearing from him or seeing from him past 2016," said Adele Bradley, 25, who attended Monday's forum.
"I look to him to keep me inspired, and I didn't want him to disappear from the spotlight."
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