Their contract with Vons, Ralphs and Albertsons expired March 6. The union says there has been no progress in the negotiations.
Members of United Food and Commercial Workers Local 770 began voting at 8 a.m. and continued through the day.
Results were expected to be released Thursday, officials said.
"We can't afford not to strike," said Jim Lirette, who works for Vons in Pasadena.
However, an authorization doesn't necessarily mean workers will walk out, but it does give the union the power to call for a strike if talks break down.
The big three supermarkets would not comment on negotiating specifics, but Albertsons called "any talk of a strike premature and unnecessary."
Vons said it was an "unnecessary distraction."
Ralphs says it's a "common tactic in negotiations and does not necessarily mean a strike will occur."
In 2003, a grocery workers strike and lockout dragged on for more than four months, costing the supermarkets an estimated $1.5 billion.
"We're trying to get our wages up, we're trying to preserve our pension, we're trying to preserve our health and welfare," said Rick Icaza, the UFCW Union Local 770 president.
An exclusive Eyewitness News poll conducted by SurveyUSA asked: "If there was a strike, would you change where you shopped?" Forty-five of Southern Californians said yes, 41 percent said no and 14 percent were not sure.
