We study the clustering of galaxies detected at $i<22.5$ in the Science Verification observations of the Dark Energy Survey (DES). Two-point correlation functions are measured using $2.3times 10^6$ galaxies over a contiguous 116 deg$^2$ region in five bins of photometric redshift width $Delta z = 0.2$ in the range $0.2 < z < 1.2.$ The impact of photometric redshift errors are assessed by comparing results using a template-based photo-$z$ algorithm (BPZ) to a machine-learning algorithm (TPZ). A companion paper (Leistedt et al 2015) presents maps of several observational variables (e.g. seeing, sky brightness) which could modulate the galaxy density. Here we characterize and mitigate systematic errors on the measured clustering which arise from these observational variables, in addition to others such as Galactic dust and stellar contamination. After correcting for systematic effects we measure galaxy bias over a broad range of linear scales relative to mass clustering predicted from the Planck $Lambda$CDM model, finding agreement with CFHTLS measurements with $chi^2$ of 4.0 (8.7) with 5 degrees of freedom for the TPZ (BPZ) redshifts. We test a linear bias model, in which the galaxy clustering is a fixed multiple of the predicted non-linear dark-matter clustering. The precision of the data allow us to determine that the linear bias model describes the observed galaxy clustering to $2.5%$ accuracy down to scales at least $4$ to $10$ times smaller than those on which linear theory is expected to be sufficient.
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