I have the EXACT scenario going on where I work, except that she doesnt blab about gangsta stuff but bizarre things ranging from her creepy medical conditions, her calls where she gets all scared that she has lung cancer and then proceeds to smoke 2 packs a day (no offense to smokers) etc etc.
What I did, was I just got some good earphones, brought some good music and now I dont have to hear her. Moreover, I earn points as the good employee who cares about the noise level while the rest of the office plots her demise.
Give it a shot.
Otherwise its practical joke time. Disconnect her computer cd rom from inside the computer so she cant play the music, or if its on a stereo, pull out the batteries or simply hide the stereo in another cubicle on another floor or building. Leave a raw fish somewhere in her cubicle....maybe under the heater or air vent. Take her chair and toss it somewhere every morning.
Or approach your management and claim that due to the excessive noise level you cannot complete your work, cannot be held accountable for its non-completion and that the volume level violates workplace health and safety standards. If management refuses to do anything, call the occupational health and safety board or equivalent and make a complaint and let them breathe down your manager's neck.
Or tell her to lower her voice and shut the hell up! The working environment is uncomfortable enough as it is...telling her off wont make anything worse.
I hope it all works out for you,
Cheers