  We report on a search for the decay K_L -> pi^0 nu nubar, carried out as a
part of E799-II, a rare K_L decay experiment at Fermilab. Within the Standard
Model, the K_L -> pi^0 nu nubar decay is dominated by direct CP violating
processes, and thus an observation of the decay implies confirmation of direct
CP violation. Due to theoretically clean calculations, a measurement of B(K_L
-> pi^0 nu nubar) is one of the best ways to determine the CKM parameter eta.
No events were observed, and we set an upper limit B(K_L -> pi^0 nu nubar) <
5.9 times 10^-7 at the 90% confidence level.
