A search for supersymmetry in the context of general gauge-mediated breaking with the lightest neutralino as the next-to-lightest supersymmetric particle and the gravitino as the lightest is presented. The data sample corresponds to an integrated luminosity of 36 pb(-1) recorded by the CMS experiment at the LHC. The search is performed by using events containing two or more isolated photons, at least one hadronic jet, and significant missing transverse energy. No excess of events at high missing transverse energy is observed. Upper limits on the signal cross section for general gauge-mediated supersymmetry between 0.3 and 1.1 pb at the 95% confidence level are determined for a range of squark, gluino, and neutralino masses, excluding supersymmetry parameter space that was inaccessible to previous experiments.