  We investigate the low-temperature thermodynamics of the spin-1/2 Heisenberg
chain with open ends. On the basis of boundary conformal field theory arguments
and numerical density matrix renormalization group calculations, it is
established that in the isotropic case the impurity susceptibility exhibits a
Curie-like divergent behavior as the temperature decreases, even in the absence
of magnetic impurities. A similar singular temperature dependence is also found
in the boundary contributions of the specific heat coefficient. In the
anisotropic case, for $1/2<\Delta<1$, these boundary quantities still show
singular temperature dependence obeying a power law with an anomalous
dimension. Experimental consequences will be discussed.
