Using a sample of 108 triggered events, produced in π−−Cu interactions at 350 GeV/c, we have identified 26 beauty events. The estimated background in this sample is 0.6 ± 0.6 events. From these data, assuming a linear A-dependence, we measure a beauty production cross section integrated over all χF of 5.7−1.1+1.3 (stat.)−0.5+0.6 (syst.) nb/N.