Molecular simulations are used to evaluate thermal resistance between crystalline silicon and a vertically oriented carbon nanotube (CNT). Without chemical bonds between CNT and Si the thermal resistance is high and its values are consistent with that measured in experiment on vertical CNT arrays. With chemical bonds the thermal resistance is reduced by two orders of magnitude demonstrating significant potential of CNT arrays for thermal management applications. The underlying mechanism for the very large effect of chemical bonding is revealed by simulations of individual phonon scattering across the interface and understood within an analytical solution of a simple spring-mass chain model.