We have carried out at Fermilab the first search for the lepton-family number violating decay K-L-->pi(0)mu(+/-)e double dagger. There were no events observed. By normalizing to K-L-->pi(+)pi(-)pi(0) decays collected simultaneously, the 90% confidence level upper limit on 1/2[BR(K-L-->pi(0)mu(+)e(-)) + BR(K-L-->pi(0)mu(-)e(+))] was determined to be 3.1 X 10(-9). (C) 1998 Published by Elsevier Science B.V. All rights reserved.