  The hemisphere soft function is calculated to order alpha_s^2. This is the
first multi-scale soft function calculated to two loops. The renormalization
scale dependence of the result agrees exactly with the prediction from
effective field theory. This fixes the unknown coefficients of the singular
parts of the two-loop thrust and heavy-jet mass distributions. There are four
such coefficients, for 2 event shapes and 2 color structures, which are shown
to be in excellent agreement with previous numerical extraction. The asymptotic
behavior of the soft function has double logs in the CF CA color structure,
which agree with non-global log calculations, but also has sub-leading single
logs for both the CF CA and CF TF nf color structures. The general form of the
soft function is complicated, does not factorize in a simple way, and disagrees
with the Hoang-Kluth ansatz. The exact hemisphere soft function will remove one
source of uncertainty on the alpha_s fits from e+e- event shapes.
