We present measurements of the time-dependent CP-violation parameters S and C in B-0 -> eta K-'(0) decays. The data sample corresponds to 384 x 10(6) B (B) over bar pairs produced by e(+)e(-) annihilation at the Upsilon(4S). The results are S = 0.58 +/- 0.10 +/- 0.03 and C = -0.16 +/- 0.07 +/- 0.03. We observe mixing-induced CP violation with a significance of 5.5 standard deviations in this b -> s penguin dominated mode.
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