  We compute the 1-jettiness soft function for the decay of a heavy quark into
a light quark jet plus colorless particles at three-loop order in
soft-collinear effective theory. The 1-jettiness measurement fixes the total
small light-cone momentum component of the soft radiation with respect to the
jet direction. This soft function is a universal ingredient to the
factorization of heavy-to-light quark decays in the limit of small 1-jettiness.
Our three-loop result is required for resummation at the N$^3$LL$^\prime$
level, e.g. near the endpoint in the photon energy spectrum of the $B \to X_s
\gamma$ decay. It is also a necessary ingredient for future calculations of
fully-differential heavy-to-light quark decay rates at N$^3$LO using the
$N$-jettiness subtraction method, e.g. for semileptonic top decays. Using our
result for the soft anomalous dimension we confirm predictions on the universal
infrared structure of QCD scattering amplitudes with a massive external quark
at three loops.
