Chris Brown's Ex Karrueche Tran -- Rihanna Doesn't Faze Me ... I Still Want Chris Back

Chris Brown's recently-dumped ex Karrueche Tran still believes she has a future with the singer -- in fact, Karrueche is telling friends, she's not gonna stop trying to get with CB just because Rihanna's back in the picture.

Sources close to Karrueche tell TMZ, she was hurt when Brown gave her the axe a few weeks ago ... but she never stopped loving him -- and now, she is on a mission to get him back.

We're told Karrueche got used to a certain level of celebrity while dating the singer, and she's not ready to "go back to being basic" -- even if that means messing around with Brown, while he's messing with RiRi.

Eventually, we're told Karrueche hopes to edge Rihanna back out of the picture.

Case in point -- Karrueche and CB were spotted hanging out together Monday in Burbank, CA ... two days after Rihanna and CB were spotted together in L.A.

As we previously reported, CB broke up with Karrueche earlier this month -- citing RiRi as the reason -- saying, "I love Karrueche very much but I don't want to see her hurt over my friendship with Rihanna."