In order to produce a neutron-rich Lambda hypernucleus for the first time, we carried out an experiment by utilizing the (pi-,K+) double charge-exchange reaction on a 10B target. We observed the production of a 10LambdaLi hypernucleus. The cross section for the Lambda bound region was found to be 11.3+/-1.9 nb/sr with the 1.2 GeV/c incident momentum, which is compared with the 10LambdaB hypernucleus production cross section, 7.8+/-0.3 microb/sr, in the (pi+,K+) reaction with a 1.05 GeV/c incident momentum beam.