The inclusive jet cross section is measured in pp collisions with a center-of-mass energy of 7 TeV at the Large Hadron Collider using the CMS experiment. The data sample corresponds to an integrated luminosity of 34 pb(-1). The measurement is made for jet transverse momenta in the range 18-1100 GeV and for absolute values of rapidity less than 3. The measured cross section extends to the highest values of jet p(T) ever observed and, within the experimental and theoretical uncertainties, is generally in agreement with next-to-leading-order perturbative QCD predictions.