We performed a search for a light pseudoscalar particle X in the decay K_{L};{0}-->pi;{0}pi;{0}X, X-->gammagamma with the E391a detector at KEK. Such a particle with a mass of 214.3 MeV/c;{2} was suggested by the HyperCP experiment. We found no evidence for X and set an upper limit on the product branching ratio for K_{L};{0}-->pi;{0}pi;{0}X, X-->gammagamma of 2.4x10;{-7} at the 90% confidence level. Upper limits on the branching ratios in the mass region of X from 194.3 to 219.3 MeV/c;{2} are also presented.