  The internal rotational dynamics of massive stars are poorly understood. If
angular momentum (AM) transport between the core and the envelope is
inefficient, the large core AM upon core-collapse will produce rapidly rotating
neutron stars (NSs). However, observations of low-mass stars suggest an
efficient AM transport mechanism is at work, which could drastically reduce NS
spin rates. Here we study the effects of the baroclinic instability and the
magnetic Tayler instability in differentially rotating radiative zones.
Although the baroclinic instability may occur, the Tayler instability is likely
to be more effective for AM transport. We implement Tayler torques as
prescribed by Fuller et al. 2019 into models of massive stars, finding they
remove the vast majority of the core's AM as it contracts between the main
sequence and helium-burning phases of evolution. If core AM is conserved during
core-collapse, we predict natal NS rotation periods of $P_{\rm NS} \approx
50-200 \, {\rm ms}$, suggesting these torques help explain the relatively slow
rotation rates of most young NSs, and the rarity of rapidly rotating
engine-driven supernovae. Stochastic spin-up via waves just before
core-collapse, asymmetric explosions, and various binary evolution scenarios
may increase the initial rotation rates of many NSs.
