  We calculate the soft function for the global event variable 1-jettiness at
next-to-next-to-leading order (NNLO) in QCD. We focus specifically on the
non-Abelian contribution, which, unlike the Abelian part, is not determined by
the next-to-leading order result. The calculation uses the known general forms
for the emission of one and two soft partons and is performed using a
sector-decomposition method that is spelled out in detail. Results are
presented in the form of numerical fits to the 1-jettiness soft function for
LHC kinematics (as a function of the angle between the incoming beams and the
final-state jet) and for generic kinematics (as a function of three independent
angles). These fits represent one of the needed ingredients for NNLO
calculations that use the N-jettiness event variable to handle infrared
singularities.
