Leah Fried, an organizer with the United Electrical Workers, said the Chicago-based vinyl window manufacturer failed to give 60 days' notice required by law before shutting down.
Workers also were angered when company officials didn't show up for a meeting Friday that had been arranged by U.S. Rep Luis Gutierrez, a Chicago Democrat, she said.
During the peaceful takeover, workers have been shoveling snow and cleaning the building, Fried said.
"We're doing something we haven't since the 1930s, so we're trying to make it work," Fried said.
Union officials said another meeting with the company is scheduled for Monday.
Representatives of Republic Windows did not immediately respond Saturday to calls and e-mails seeking comment.
Police spokeswoman Laura Kubiak said authorities were aware of the situation and officers were patrolling the area.
Crain's Chicago Business reported that the company's monthly sales had fallen to $2.9 million from $4 million during the past month. In a memo to the union, obtained by the business journal, Republic CEO Rich Gillman said the company had "no choice but to shut our doors."
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