CHICAGO — Janet Yellen, the Federal Reserve chairwoman, devoted more than an hour last week talking by telephone with three Chicago area residents struggling to find jobs.

On Monday, she made their stories the centerpiece of the first public speech in her new job, delivering a strong statement about her concern over unemployment, her conviction that the Fed has the power to help, and her determination to do so.

“It is my hope,” Yellen told a conference hosted by the Federal Reserve Bank of Chicago, “that the courageous and determined working people I have told you about today, and millions more, will get the chance they deserve to build better lives.”

The speech offered a rebuttal to economists, including some Fed officials, who see evidence that the central bank is approaching the limits of its ability to improve labor market conditions. It also leaned against recent indications that Fed officials might be considering a faster retreat from their economic stimulus campaign.

Yellen said that even now, almost five years after the official end of the Great Recession, it remains harder for Americans to find jobs than in the midst of a typical downturn. For those who are working, wages are rising more slowly than usual.

“There remains no doubt that the economy and the job market are not back to normal health,” Yellen said. “The recovery still feels like a recession to many Americans and it also looks that way in some economic statistics.”

She said the Fed’s commitment to economic stimulus remained “strong.”

The core of Yellen’s speech was devoted to a central issue confronting Fed officials as they seek to calibrate their efforts to stimulate the economy. Employment dropped sharply during the recession and has barely recovered. The unemployment rate has fallen because it counts only people who are looking for work, and a lot of people have given up entirely.