Supervisors Hilda Solis and Holly Mitchell co-authored the motion calling for a temporary "urgency" ordinance that would apply to store chains that are publicly traded or have at least 300 employees nationwide and more than 10 employees per store.
The temporary measure is aimed at rewarding employees on the frontlines serving the public during the coronavirus pandemic.
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The "hero pay" measure only applies to employees of retailers operating in unincorporated areas of L.A. County.
"These employers employ a labor workforce that consists of low-wage workers who have been disproportionately impacted by the economic fallout of this pandemic, with nearly half reporting challenges paying their bills and roughly a third having trouble paying their rent or mortgage," the motion states.
If approved, the ordinance would be expected to stay in force for 120 days. Solis and Mitchell also want to consider whether the rule could apply to stores in incorporated cities.
In December, the Long Beach City Council passed a resolution that would require "hero pay" for all frontline grocery workers.
RELATED: LA considers 'hero pay' for grocery store workers
City News Service contributed to this report.