Chris Browns GF Karrueche -- I'm Scared to DEATH of Rihanna's Crazy Fans

Chris Browns GF is scared to leave her house without bodyguards by her side -- and she's telling friends, it's all because Rihanna's crazy fans are threatening to kill her.

In case you missed it -- there was a lot of speculation last week that Rihanna dissed Karrueche Tran on Twitter -- posting a pic of a bag of rice cakes wearing sunglasses ... with the caption, "Ima a make u my bitch."

The joke -- Karrueche's Vietnamese ... rice cakes ... etc.

But several of Rihanna's fans took the joke one step too far -- unleashing an avalanche of violent threats on Karrueche ... like "I hope Rihanna beat the dog shit outa yo ass!" ... "Watch yo back" ... and "I will kill you."

Rihanna never admitted the rice cake jab was directed at Karrueche -- but sources close to Karrueche tell TMZ, she now refuses to leave her house without Chris Brown's hired muscle by her side.

As for Karrueche's infamous BF -- we're told CB is 100% supportive of his new lady ... despite getting closewith Rihanna recently ... and is urging her not to worry.

The real lesson here -- dont date Chris Brown.