We present a quantitative analysis of the correlation between quasi-localized, low energy vibrational modes and structural relaxation events in computer simulations of a quiescent, thermal polymer glass. Our results extend previous studies on glass forming binary mixtures in 2D, and show that the soft modes identify regions that undergo irreversible rearrangements with up to 7 times the average probability. We study systems in the supercooled- and aging-regimes and discuss temperature- as well as age-dependence of the correlation. In addition to the location of rearrangements, we find that soft modes also predict their direction on the molecular level. The soft regions are long lived structural features, and the observed correlations vanish only after >50% of the system has undergone rearrangements.