Chief Keef Sued -- Pay Your Rent ... Or Get the Hell Out

Chief Keef is swimming in cash but he's not handing any of it over to his landlord ... who claims the rap prodigy owes almost $10k in back rent.

Georghe Simoniak-Sas filed a lawsuit against Keef -- real name Keith Cozart -- and Keef's uncle. In docs, Georghe says Keef hasn't coughed up rent for the months of July or August ($4,700 /month) on the Illinois mansion he's renting ... but continues to live there.

Georghe says enough is enough ... he's suing for eviction and to collect $9,400 in back rent.

As for the digs ... 5,100 square feet, 6 bedrooms, 5.5 baths. Valued at over $1 million.

Which we're pretty sure Keef can afford.