We present a measurement of the time-dependent CP asymmetry for the neutral B-meson decay B0-->phiK0. We use a sample of approximately 114 x 10(6) B-meson pairs taken at the Upsilon(4S) resonance with the BABAR detector at the PEP-II B-meson factory at SLAC. We reconstruct the CP eigenstates phiK0S and phiK0L, where phi-->K+K-, K0S-->pi+pi-, and K0L is observed via its hadronic interactions. The other B meson in the event is tagged as either a B0 or Bbar0 from its decay products. The values of the CP-violation parameters are SphiK=0.47+/-0.34(stat)+0.08-0.06(syst) and CphiK=0.01+/-0.33(stat)+/-0.10(syst).