We present ab initio calculations concerning the bond scission rate in a polyethylene chain. The energy barrier for scission is calculated both by using an effective potential scheme based on ab initio data and from the ab initio transition state itself. In the latter case the prefactor for scission is calculated. In both methods the relaxation of the polymer chain is taken into account, leading to a strong strain dependence of the energy barrier. The two schemes agree quantitatively. The barrier is reduced from 3.9 eV at zero strain to 1.7 eV at a strain of 5%. The calculated scission rate is used to estimate the strength of a polyethylene fiber consisting of perfectly aligned, independent chains in a constant strain rate experiment resulting in 18 GPa at a strain of 8%. This value of the ultimate strength is a factor 2 larger than found in experiments. This contrasts previously reported quantum chemical calculations, which reported values a factor 5-10 larger than the experimental values.