We present the first measurements of clustering in the Sloan Digital SkySurvey (SDSS) galaxy redshift survey. Our sample consists of 29,300galaxies with redshifts5700kms-1<=cz<=39,000kms-1, distributed inseveral long but narrow (2.5d-5°) segments, covering 690deg2. For the full, flux-limited sample, the redshift-spacecorrelation length is approximately 8 h-1 Mpc. Thetwo-dimensional correlation function ξ(rp,π) showsclear signatures of both the small-scale, ``fingers-of-God'' distortioncaused by velocity dispersions in collapsed objects and the large-scalecompression caused by coherent flows, though the latter cannot bemeasured with high precision in the present sample. The inferredreal-space correlation function is well described by a power law,ξ(r)=(r/6.1+/-0.2h-1Mpc)-1.75+/-0.03, for0.1h-1Mpc<=r<=16h-1Mpc. The galaxy pairwisevelocity dispersion is σ12~600+/-100kms-1for projected separations0.15h-1Mpc<=rp<=5h-1Mpc. When wedivide the sample by color, the red galaxies exhibit a stronger andsteeper real-space correlation function and a higher pairwise velocitydispersion than do the blue galaxies. The relative behavior ofsubsamples defined by high/low profile concentration or high/low surfacebrightness is qualitatively similar to that of the red/blue subsamples.Our most striking result is a clear measurement of scale-independentluminosity bias at r<~10h-1Mpc: subsamples with absolutemagnitude ranges centered on M*-1.5, M*, andM*+1.5 have real-space correlation functions that areparallel power laws of slope ~-1.8 with correlation lengths ofapproximately 7.4, 6.3, and 4.7 h-1 Mpc, respectively.