Chris Brown BUYS HOUSE For Karrueche Tran: [Photos]

HMM RIHANNA got to faint if she hears this...It definitly pays to be Chris Brown's girlfriend, because Karrueche Tran now has enough Hollywood heat to rent a beautiful home in one of the hippest L.A. neighbour hoods.

We're told Karrueche Tran is plunking down $4,600-a-month for a house in the heart of West Hollywood. The house is often adorned by Brown's various Lambos.

It seems like a hefty price to pay for someone with no full-time gig ... but she's been scoring some lucrative appearances at nightclubs recently -- thanks to Chris, of course.