We present evidence for D0-D(0) mixing in D(0)-->K(+)pi(-) decays from 384 fb(-1) of e(+)e(-) colliding-beam data recorded near square root s=10.6 GeV with the BABAR detector at the PEP-II storage rings at the Stanford Linear Accelerator Center. We find the mixing parameters x('2)=[-0.22+/-0.30(stat)+/-0.21(syst)] x 10(-3) and y(')=[9.7+/-4.4(stat)+/-3.1(syst)] x 10(-3) and a correlation between them of -0.95. This result is inconsistent with the no-mixing hypothesis with a significance of 3.9 standard deviations. We measure R(D), the ratio of doubly Cabibbo-suppressed to Cabibbo-favored decay rates, to be [0.303+/-0.016(stat)+/-0.010(syst)]%. We find no evidence for CP violation.