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The core rotation rates of massive stars have a substantial impact on the nature of core collapse supernovae and their compact remnants. We demonstrate that internal gravity waves (IGW), excited via envelope convection during a red supergiant phase or during vigorous late time burning phases can have a profound impact on the rotation rate of the pre-SN core. In typical ($10 M_\odot \lesssim M \lesssim 20 M_\odot$) supernova progenitors, IGW can substantially spin down the core, leading to iron core rotation periods $(P_{\rm Fe} \gtrsim 130 \, {\rm s})$. Angular momentum (AM) conservation during the supernova would entail minimum NS rotation periods of $P_{\rm NS} \gtrsim 7 \, {\rm ms}$. In most cases, the combined effects of magnetic torques and IGW AM transport likely lead to substantially slower rotation periods. However, stochastic AM fluxes carried into the core by IGW during shell burning phases also entail a maximum core rotation period. We estimate $P_{\rm Fe} \lesssim 2 \, {\rm hr}$ in most core collapse supernova progenitors, and a corresponding spin period of $P_{\rm NS} \lesssim 300 \, {\rm ms}$ for the newborn neutron star. Therefore, in the event of efficient core spin-down via waves/magnetic
torques, torques in previous stages of evolution, stochastic IGW spin-up during shell O/Si burning may primarily determine the initial rotation rate of ordinary pulsars.