Campaign officials say the 29-year-old aide, Alex Okrent, worked in the campaign's paid media department, which handles advertising.
The Chicago Sun-Times reports that paramedics treated Okrent at the campaign headquarters and then took him to Northwestern Memorial Hospital, where he was pronounced dead.
Obama's campaign says the president called Okrent's parents to offer his condolences. Okrent was a field organizer on Obama's 2004 Senate campaign and then worked on Obama's 2008 presidential campaign.
The president later spoke with other campaign staffers in a conference call to offer his condolences.