We present a measurement of the time-dependent CP-violating (CPV) asymmetries in B0-->K(0)(S)pi(0) decays based on 124x10(6) Upsilon(4S)-->BB decays collected with the BABAR detector at the PEP-II asymmetric-energy B factory at SLAC. In a sample containing 122+/-16 signal decays, we obtain the magnitudes of the direct CPV asymmetry CK(0)(S)(pi(0))=0.40(+0.27)(-0.28)+/-0.09 and of the CPV asymmetry in the interference between mixing and decay SK(0)(S)(pi(0))=0.48(+0.38)(-0.47)+/-0.06 where the first error is statistical and the second systematic.