  Daya Bay presents the first measurement of cosmogenic $^8$He isotope
production in liquid scintillator, using an innovative method for identifying
cascade decays of $^8$He and its child isotope, $^8$Li. We also measure the
production yield of $^9$Li isotopes using well-established methodology. The
results, in units of 10$^{-8}\mu^{-1}$g$^{-1}$cm$^{2}$, are 0.307$\pm$0.042,
0.341$\pm$0.040, and 0.546$\pm$0.076 for $^8$He, and 6.73$\pm$0.73,
6.75$\pm$0.70, and 13.74$\pm$0.82 for $^9$Li at average muon energies of
63.9~GeV, 64.7~GeV, and 143.0~GeV, respectively. The measured production rate
of $^8$He isotopes is more than an order of magnitude lower than any other
measurement of cosmogenic isotope production. It replaces the results of
previous attempts to determine the ratio of $^8$He to $^9$Li production that
yielded a wide range of limits from 0 to 30\%. The results provide future
liquid-scintillator-based experiments with improved ability to predict
cosmogenic backgrounds.
