Arrays of C60 molecules nested inside single-walled nanotubes represent a class of nanoscale materials having tunable properties. We report electronic measurements of this system made with a scanning tunneling microscope and demonstrate that the encapsulated C60 molecules modify the local electronic structure of the nanotube. Our measurements and calculations also show that a periodic array of C60 molecules gives rise to a hybrid electronic band, which derives its character from both the nanotube states and the C60 molecular orbitals.