The thermal conductivity kappa of two untwinned single crystals of YBa
2Cu3O7-delta (T-C=91 K) has been measured along the a- (kappa(a)) and
b-axis (kappa(b)) for 0.1K<T<80K and in magnetic fields B less than or
equal to 6 T (B parallel to j(th)). For T<T-C a maximum in kappa is f
ound for both directions (kappa(a): T(max)approximate to 45 K, kappa(b
): T(max)approximate to 54 K). Foe T>30 K kappa(b) is found to be larg
er than kappa(a), while for 0.2 K<T<30 K, kappa(a)=kappa(b) within exp
erimental resolution. At the lowest temperatures accessible in our exp
eriment kappa(b) asymptotically approaches a linear in T dependence po
inting towards an additional contribution of the thermal conductivity
parallel to the direction of the Cu-O chains at T<0.3 K. Applying a ma
gnetic field (B=6 T) leaves kappa(a) (0.2K<T<30K) and kappa(b) (0.1 K<
T<30 K) unchanged. These findings are discussed in the light of a supe
rposition of phononic and electronic thermal conductivities and their
relevance to the recently proposed d-wave scenario for unconventional
superconductivity in oxide superconductors.