  We analyze the collective mode spectrum of graphene nanoribbons within the
random phase approximation. In the undoped case, only metallic armchair
nanoribbons support a propagating plasmon mode. Landau damping of this mode is
shown to be suppressed through the chirality of the single particle
wavefunctions. We argue that undoped zigzag nanoribbons should not support
plasmon excitations because of a broad continuum of particle-hole excitations
associated with surface states, into which collective modes may decay. Doped
nanoribbons have properties similar to those of semiconductor nanowires,
including a plasmon mode dispersing as $q\sqrt{-\ln qW}$ and a static
dielectric response that is divergent at $q=2k_F$.
