Evidence for the neutron-rich hypernucleus H-6(Lambda) is presented from the FINUDA experiment at DA Phi NE, Frascati, studying (pi(+), pi(-)) pairs in coincidence from the (K) over bar (-)(stop) + Li-6 -> H-6(Lambda) + pi(+) production reaction followed by H-6(Lambda) -> He-6 + pi(-) weak decay. The production rate of H-6(Lambda) undergoing this two-body pi(-) decay is determined to be (2.9 +/- 2.0) x 10(-6)/K-stop(-). Its binding energy, evaluated jointly from production and decay, is B-Lambda(H-6(Lambda)) = (4.0 +/- 1.1) MeV with respect to 5H + Lambda. A systematic difference of (0.98 +/- 0.74) MeV between B-Lambda values derived separately from decay and from production is tentatively assigned to the H-6(Lambda) 0(g.s)(+) excitation.