An employee and guest of the Congress Hotel testified in support of the ordinance.
Some workers there have been on strike for six years.
Supporters believe customers have a right to know., saying a strike can affect service.
Opponents say such an ordinance could affect Chicago's ability to draw conventions and other tourists.
"We can handle this in different ways. We don't need an ordinance; we don't need a law to do this," Jerry Roper, of the Chicagoland Chamber of Commerce, said.
"I was resigned, after talking with folks on the picket line, that I was going to cross the picket line. But I was not happy about it. I'm a supporter of workers' rights," Chicago visitor Jim Kuhn said.
Council members did not take action on the ordinance Monday. A similar ordinance was proposed in 2005, but was not passed.