The angular distribution of galaxies encodes a wealth of informationabout large-scale structure. Ultimately, the Sloan Digital Sky Survey(SDSS) will record the angular positions of order of 108galaxies in five bands, adding significantly to the cosmologicalconstraints. This is the first in a series of papers analyzing arectangular stripe of 2.5d×90deg from early SDSS data.We present the angular correlation function for galaxies in fourseparate magnitude bins on angular scales ranging from 0.003d to15°. Much of the focus of this paper is on potential systematiceffects. We show that the final galaxy catalog-with the mask accountingfor regions of poor seeing, reddening, bright stars, etc.-is free fromexternal and internal systematic effects for galaxies brighter thanr*=22. Our estimator of the angular correlation functionincludes the effects of the integral constraint and the mask. The fullcovariance matrix of errors in these estimates is derived using mockcatalogs with further estimates using a number of other methods. Basedon observations obtained with the Sloan Digital Sky Survey.