With a germanium detector array (Hyperball), we observed two gamma-ray peaks corresponding to the two transitions (5/2(+)-->1/2(+) and 3/2(+)-->1/2(+)) in the (9)(Lambda)Be hypernucleus which was produced by the 9Be(K-,pi(-)) reaction. The energies of the gamma rays are 3029 +/- 2 +/- 1 keV and 3060 +/- 2 +/- 1 keV. The energy difference was measured to be 31.4(+2.5)(-3.6) keV, which indicates a very small Lambda-spin-dependent spin-orbit force between a Lambda and a nucleon. This is the smallest level splitting by far ever measured in a hypernucleus.