We present a search for anomalous components of the quartic gauge boson coupling WW{\gamma}{\gamma} in events with an electron, a positron and missing transverse energy. The analyzed data correspond to 9.7 fb^-1 of integrated luminosity collected by the D0 detector in ppbar collisions at sqrt(s) = 1.96 TeV. The presence of anomalous quartic gauge couplings would manifest itself as an excess of boosted WW events. No such excess is found in the data, and we set the most stringent limits to date on the anomalous coupling parameters a_0^W and a_C^W. When a form factor with Lambda_cutoff = 0.5 TeV is used, the observed upper limits at 95 % C.L. are |a_0^W/Lambda^2|< 0.0025 GeV^-2 and |a_C^W/Lambda^2| < 0.0092 GeV^-2.