We investigate neutron star moments of inertia from Bayesian posterior probability distributions of the nuclear equation of state that incorporate information from microscopic many-body theory and empirical data of finite nuclei. We focus on PSR J0737-3039A and predict that for this 1.338 M neutron star the moment of inertia lies in the range 1.04 × 10 45 g cm 2 < I < 1.51 × 10 45 g cm 2 at the 95% credibility level, while the most probable value for the moment of inertia isĨ = 1.36×10 45 g cm 2 . Assuming a measurement of the PSR J0737-3039A moment of inertia to 10% precision, we study the implications for neutron star radii and tidal deformabilities. We also determine the crustal component of the moment of inertia and find that for typical neutron star masses 1.3M < M < 1.5M the crust contributes 1 − 6% of the total moment of inertia, below what is needed to explain large pulsar glitches in the scenario of strong neutron entrainment.