More than 100 employees walked off the job on June 9, Teamsters Local 705 said.
Teamsters said the company "broke the law and refused to bargain in good faith."
Chicago Mayor Brandon Johnson and Illinois U.S. Representative Jesús "Chuy" García joined the workers.
Workers are demanding safer working conditions, guaranteed break times and affordable healthcare.
"This union and this strike is leading the way to ensure that this country knows that workers run this country," Johnson said.
Teamsters said workers also want measures to "prevent ICE from entering the workplace without a judicial warrant."
"All they want is a far deal that enables them to work and to keep providing and to retire with dignity," Garcia said.
The strike happened at Mauser Packaging Solutions facility in Little Village.
ABC7 reached out to Mauser and has yet to hear back.
Mayor Johnson joins Mauser packaging picket line