  Hadronic annihilation rate of $1^{+-}$ heavy quarkonium is given to
next-to-leading order in $\alpha_s$ and leading order in $v^2$ using a recently
developed factorization formalism which is based on NRQCD. The result includes
both the annihilation of P-wave color-singlet $Q\bar{Q}$ component, and the
annihilation of S-wave color-octet $Q\bar{Q}$ component of the quarkonium. The
notorious infrared divergences due to soft gluons, i.e., the Logarithms
associated with the binding energy, encountered in previous perturbative
calculations of $1^{+-}$ quarkonium decays are found to be explicitly
cancelled, and a finite result for the decay width to order $\alpha_s^3$ is
then obtained.
