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Internal gravity waves (IGW) constitute a powerful energy and AM transport mechanism. Several studies (\citealt{kumar:97,zahn:97,kumar:99,talon:02,talon:03,talon:05,talon:08,charbonnel:05,denissenkov:08,fullerwave:14}, hereafter F14) have found that convectively generated IGW can redistribute large quantities of AM within low-mass stars. IGW may partially account for the rigid rotation of the Sun's radiative interior and the slow rotation of red giant cores, although magnetic torques are also likely to be important (\citealt{denissenkov:08}, F14). IGW may also be important in more massive stars, and \cite{lee:14} found that convectively generated IGW in Be-type stars may instigate outbursts that expel mass into the decretion disk.  Convectively excited IGW may also have a powerful strong  influence on the evoution of massive stars nearing CC. Indeed, after core carbon exhaustion, waves are the most effective energy transport mechanism within radiative zones, as photons are essentially frozen in and neutrinos freely stream out. In two recent papers, \citet{quataert:12} and \citet{shiode:14} (hereafter QS12 and SQ14) showed that the prodigious power carried by convectively excited waves (on the order of $10^{10} L_\odot$ during Si burning) can sometimes unbind a large amount of mass near the stellar surface, and may substantially alter the pre-collapse stellar structure. IGW are ubiquitously seen in simulations of late burning stages \citep{meakin:06,meakina:07,meakinb:07}, although the simulations do not run long enough to determine their long-term impact. In this paper, we examine AM transport due to convectively excited IGW within massive stars, focusing primarily on AM transport due to late burning stages (He, C, O, and Si burning). We find that IGW are generally capable of redistributing large amounts of AM before CC despite the short stellar evolution time scales. IGW emitted from convective shells propagate into the radiative core and may be able to substantially slow its rotation, although magnetic torques may be more important. In the case of powerful core spin-down via magnetic torques, we show that stochastic influxes of AM via IGW set a minimum core rotation rate which is comparible with the broad distribution of low rotation rates ($P \lesssim 500 \,{\rm ms}$) observed for most young NSs.