CIARA BEING SUED FOR SKIPPING SHOW!

Ciara is being sued by a West Hollywood gay bar ... which claims the singer left them high and dry when she backed out of a gay event during L.A. Pride week ... TMZ has learned.

The nightclub going after Ciara is "The Factory" -- which, according to one Yelp reviewer, is always packed with "gays" who "know how to party."

According to the lawsuit, obtained by TMZ, Ciara signed a $10,000 deal to appear at The Factory on June 7 (tonight) ... one day before she's supposed to perform on the main stage at the 2013 L.A. Pride parade.

Factory says Ciara had mentioned that she couldn't "perform" at Factory due to restrictions in her contract with the L.A. Pride event ... but made it seem like making an "appearance" would be totally kosher.

But Factory says ... Ciara unexpectedly pulled the plug on the whole thing on June 3, leaving the nightclub without a star for its big Friday night pre-gay parade bash.

Now, Factory is suing Ciara for breach of contract -- and want her to pay for all the money the club spent to promote her appearance PLUS the cash they're losing out on thanks to Ciara's last-minute bail

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