It's over a proposal to change their work shifts and healthcare benefits.
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Employees at the bakery at 73rd Street and Kedzie Avenue walked off the job and were out picketing Thursday night.
Union employees are in contract negotiations with Nabisco's parent company, Mondelez.
BCTGM Local 1 members joined workers in Oregon, Colorado and Virginia in the strike.
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"Nabisco has long profited from the loyalty and dedication of its U. S. workers and the exploitation of its employees in Mexico," BCTGM International President Anthony Shelton said. "By taking this action, Nabisco workers in all four locations are saying strong and clear: stop exporting our jobs to Mexico and end your demands for contract concessions. The BCTGM will take all appropriate action necessary in order to reach a contract settlement that treats Nabisco workers fairly and equitably."
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Mondelez said it was disappointed in its workers' decision to strike.
"Our goal has been - and continues to be - to bargain in good faith with the BCTGM leadership across our U.S. bakeries and sales distribution facilities to reach new contracts that continue to provide our employees with good wages and competitive benefits, including quality, affordable healthcare, and company-sponsored Enhanced Thrift Investment 401(k) Plan, while also taking steps to modernize some contract aspects which were written several decades ago," it said.
The company said it activated its "robust business continuity plan" and is committed to continuing to supply snacks to retailers and consumers.