Evidence for the neutron-rich hypernucleus (Λ)(6)H is presented from the FINUDA experiment at DAΦNE, Frascati, studying (π+,π-) pairs in coincidence from the K(stop)(-) + (6)Li →(Λ)(6)H + π+ production reaction followed by (Λ)(6)H → (6)He + π- weak decay. The production rate of (Λ)(6) undergoing this two-body π- decay is determined to be (2.9 ± 2.0) × 10(-6)/K(stop)(-). Its binding energy, evaluated jointly from production and decay, is BΛ((Λ)(6)H) = (4.0 ± 1.1) MeV with respect to (5)H+Λ. A systematic difference of (0.98 ± 0.74) MeV between BΛ values derived separately from decay and from production is tentatively assigned to the (Λ)(6)H 0(g.s.)(+) → 1+ excitation.