We report measurements of the in-plane thermal conductivity kappa of the stoichiometric underdoped cuprate YBa2Cu4O8 (Y124) below 1 K. kappa(T) is shown to follow a simple phononic T3 dependence at the lowest temperature T for both current directions, with a negligible linear quasiparticle contribution. This observation is in marked contrast with behavior reported in optimally doped cuprates, and implies that extended zero-energy (or low-energy) quasiparticles are absent in Y124.