The Laser Interferometer Gravitational Wave Observatory ( LIGO ) has performed a third science run with much improved sensitivities of all three interferometers .
We present an analysis of approximately 200 hours of data acquired during this run , used to search for a stochastic background of gravitational radiation .
We place upper bounds on the energy density stored as gravitational radiation for three different spectral power laws .
For the flat spectrum , our limit of \Omega _ { 0 } < 8.4 \times 10 ^ { -4 } in the 69-156 Hz band is \sim 10 ^ { 5 } times lower than the previous result in this frequency range .