Graphene and carbon nanotubes (CNTs) are fascinating materials, both scientifically and technologically, due to their exceptional properties and potential use in applications ranging from high-frequency electronics to energy storage devices. This manuscript introduces a hybrid structure consisting of graphitic foliates grown along the length of aligned multiwalled CNTs. The foliate density and layer thickness vary as a function of deposition conditions, and a model is proposed for their nucleation and growth. The hybrid structures were studied using electron microscopy and Raman spectroscopy. The foliates consist of edges that approach the dimensions of graphene and provide enhanced charge storage capacity. Electrochemical impedance spectroscopy indicated that the weight-specific capacitance for the graphenated CNTs was 5.4× that of similar CNTs without the graphitic foliates. Pulsed charge injection measurements demonstrated a 7.3× increase in capacitance per unit area. These data suggest that this unique structure integrates the high surface charge density of the graphene edges with the high longitudinal conductivity of the CNTs and may have significant impact in charge storage and related applications.