Dispersing 1D bands have been observed for the first time in an organic conductor by high resolution photoemission experiments on TTF-TCNQ (tetrathiafulvalene-tetracyanoquinodimethane). Their properties are extremely unusual: the bandwidth is much larger than traditional estimates, and the quasiparticle states are strongly renormalized, with no weight at the chemical potential. A deep pseudogap around the Fermi energy persists, and even increases, up to room temperature. We also report a direct determination of k(F) in this material, and the observation of the opening of a Peierls gap in the low-temperature charge density wave phase.