We present a search for a narrow resonance in the inclusive diphoton final state using 2.7 fb-1 of data collected with the D0 detector at the Fermilab Tevatron ppbar Collider. We observe good agreement between the data and the background prediction, and set the first 95% C.L. upper limits on the production cross section times the branching ratio for decay into a pair of photons for resonance masses between 100 and 150 GeV. This search is also interpreted in the context of several models of electroweak symmetry breaking with a Higgs boson decaying into two photons.