The description of growth at vicinal surfaces leads to an anisotropic generalization of the Kardar- Parisi-Zhang equation [Phys. Rev. Lett. 56, 889 (1986)l which is investigated by a dynamical renormalization calculation. If the nonlinear terms have opposite signs parallel and perpendicular to the average step direction, the roughness is only logarithmic. This should be the case, e.g., for step-flow growth. As the temperature is lowered so that island formation on the terraces becomes significant, a sharp morphological transition to algebraic roughness is predicted.