The first dedicated experiment for the rare kaon decay K-L(0)->pi(0)nu nu has been performed by the E391a Collaboration at the KEK 12-GeV proton synchrotron. A new upper limit of 2.1x10(-7) at the 90% confidence level was set for the branching ratio of the decay K-L(0)->pi(0)nu nu using about 10% of the data collected during the first period of data taking.