The differential cross section for the inclusive production of isolated prompt photons has been measured as a function of the photon transverse energy E-T(Gamma) in pp collisions at root s 7 TeV using data recorded by the CMS detector at the LHC. The data sample corresponds to an integrated luminosity of 2.9 pb(-1). Photons are required to have a pseudorapidity vertical bar eta(gamma)vertical bar < 1.45 and E-T(Gamma) > 21 GeV, covering the kinematic region 0.006 < x(T) < 0.086. The measured cross section is found to be in agreement with next-to-leading-order perturbative QCD calculations.