  We report measurements of the in-plane thermal conductivity ($\kappa$) of
YBa_2Cu_4O_8 (Y-124) single crystals in the temperature range $4K\leq T\leq
300K$ and compare them with previous results on YBa_2Cu_3O_{6+x} (Y-123). For
transport perpendicular to the CuO chains, $\kappa_a(300K)\simeq 10$W/mK, and
along the chains, $\kappa_b(300K)\simeq 40$W/mK. The temperature dependence of
$\kappa$ for both transport directions is much stronger than in
YBa_2Cu_3O_{6+x} (Y-123), indicative of substantially superior lattice heat
conduction in Y-124, and resulting in maximum values for $\kappa$ at $T\sim
20$K exceeding 200W/mK. The data imply a surprisingly large anisotropy in the
lattice conduction. $\kappa_a$ and $\kappa_b$ are enhanced in the
superconducting state as in other cuprates. The magnitude and anisotropy of the
enhancement are discussed and compared to those of Y-123.
