The Laser Interferometer Gravitational-Wave Observatory 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 omega0 < 8.4 x 10(-4) in the 69-156 Hz band is approximately 10(5) times lower than the previous result in this frequency range.