We investigate the clustering of high redshift galaxies in five variants of the cold dark matter (CDM) scenario, using hydrodynamic cosmological simulations that resolve the formation of systems with circular velocities $v_c \geq 100 \kms$ ($��=1$) or $v_c \geq 70 \kms$ ($��=0.4$). Although the five models differ in their cosmological parameters and in the shapes and amplitudes of their mass power spectra, they predict remarkably similar galaxy clustering at $z=2$, 3, and 4. The galaxy correlation functions show almost no evolution over this redshift range, even though the mass correlation functions grow steadily in time. Despite the fairly low circular velocity threshold of the simulations, the high redshift galaxies are usually highly biased tracers of the underlying mass distribution; the bias factor evolves with redshift and varies from model to model. Predicted correlation lengths for the resolved galaxy population are $2-3\hmpc$ (comoving) at $z=3$. More massive galaxies tend to be more strongly clustered. These CDM models have no difficulty in explaining the strong observed clustering of Lyman-break galaxies, and some may even predict excessive clustering. Because the effects of bias obscure differences in mass clustering, it appears that Lyman-break galaxy clustering will not be a good test of cosmological models but will instead provide a tool for constraining the physics of galaxy formation.

33 pages, 10 figures, AAS LaTeX (aaspp4.sty), submitted to ApJ