In a data sample of four million hadronic Z decays collected with the ALEPH detector at LEP, four Λb baryon candidates are exclusively reconstructed in the Λb → Λc+π− channel, with the Λc+ decaying into pK−π+, , or Λπ+π+π−. The probability of the observed signal to be due to a background fluctuation is estimated to be 4.2 × 10−4. The mass of the Λb is measured to be 5614±21 (stat.) ± 4 (syst.) MeV/c2.