  We consider rapidly rotating black holes and neutron stars in dilatonic
Einstein-Gauss-Bonnet (EGBd) theory and determine their quadrupole moments,
which receive a contribution from the dilaton. The quadrupole moment of EGBd
black holes can be considerably larger than the Kerr value. For neutron stars,
the universality property of the $\hat I$-$\hat Q$ relation between the scaled
moment of inertia and the scaled quadrupole moment appears to extend to EGBd
theory.
