We report a search for the charmless hadronic decay B-0 -> eta pi(0) with a data sample corresponding to an integrated luminosity of 694 fb(-1) containing 753 x 10(6) BB pairs. The data were collected by the Belle experiment running on the Upsilon(4S) resonance at the KEKB e(+)e(-) collider. We measure a branching fraction B(B-0 > eta pi(0)) = (4.1(-1.5-0.7)(+1.75+0.5)) x 10(-7), where the first unceminty is statistical and the second is systematic. Our measurement gives an upper limit of beta(B-0 -> n pi(0)) < 6.5 x 10(-7) at 90% confidence level. The signal has a significance of 3.0 standard deviations and constitutes the first evidence for this decay mode.