We present results on the clustering of galaxies in the Stromlo-APM redshift survey, which consists of 1787 galaxies sampled at a rate of 1 in 20 at random from the APM Galaxy Survey to a magnitude limit of b(J) = 17.15. An analysis of counts in cells, and a direct estimate of the two-point correlation function, indicate more large-scale structure than expected in a biased, scale-invariant, OMEGA = 1, cold dark matter (CDM) model. Unbiased OMEGA = 1 CDM models (which are compatible with the COBE microwave background anisotropy measurements) are allowed by our observations because peculiar motions enhance the amplitude of the clustering pattern measured in redshift space on large scales. However, consistency between the redshift survey results and the angular two-point correlation function determined from the APM Galaxy Survey favors biased, or low-density, models with enhanced clustering in real space compared with standard CDM.