  High-energy tau neutrinos are rarely produced in atmospheric cosmic-ray
showers or at cosmic particle accelerators, but are expected to emerge during
neutrino propagation over cosmic distances due to flavor mixing. When high
energy tau neutrinos interact inside the IceCube detector, two spatially
separated energy depositions may be resolved, the first from the charged
current interaction and the second from the tau lepton decay. We report a novel
analysis of 7.5 years of IceCube data that identifies two candidate tau
neutrinos among the 60 ``High-Energy Starting Events'' (HESE) collected during
that period. The HESE sample offers high purity, all-sky sensitivity, and
distinct observational signatures for each neutrino flavor, enabling a new
measurement of the flavor composition. The measured astrophysical neutrino
flavor composition is consistent with expectations, and an astrophysical tau
neutrino flux is indicated at 2.8$\sigma$ significance.
