The inclusive cross section for charged-D* production by 205-GeV/c π− mesons incident on a beryllium target was measured with a two-arm spectrometer triggered by prompt muons. Using the mass-difference technique often employed in D* studies, a signal of 31±11 charged D*’s was isolated; it includes contributions from both the D*+ and D*− charged modes in correlation with triggering muons of the proper charge. This corresponds to an inclusive charged-D* production cross section of 220±77−57+77 μb per Be nucleus or 24±9−6+9 μb per nucleon when the cross section is scaled linearly with atomic mass number. The first error is statistical and the second is systematic.