A search for large extra spatial dimensions via virtual-graviton exchange in the diphoton channel has been carried out with the CMS detector at the LHC. No excess of events above the standard model expectations is found using a data sample collected in proton-proton collisions at root s = 7TeV and corresponding to an integrated luminosity of 36 pb(-1). New lower limits on the effective Planck scale in the range of 1.6-2.3TeV at the 95\% confidence level are set, providing the most restrictive bounds to date on models with more than two large extra dimensions.