Data from the LIGO Livingston interferometer and the ALLEGRO resonant-bar detector, taken during LIGO’s fourth science run, were examined for cross correlations indicative of a stochastic gravitational-wave background in the frequency range 850–950 Hz, with most of the sensitivity arising between 905 and 925 Hz. ALLEGRO was operated in three different orientations during the experiment to modulate the relative sign of gravitational-wave and environmental correlations. No statistically significant correlations were seen in any of the orientations, and the results were used to set a Bayesian 90% confidence level upper limit of Ω_gw(f)≤1.02, which corresponds to a gravitational-wave strain at 915 Hz of 1.5×10^-23Hz^-1/2. In the traditional units of h_100^2Ω_gw(f), this is a limit of 0.53, 2 orders of magnitude better than the previous direct limit at these frequencies. The method was also validated with successful extraction of simulated signals injected in hardware and software.