  Using Bethe-ansatz solutions, we uncover a well-defined continuum in
dynamical structure factor $S^{+-}(k,\omega)$ of the spin-1/2 antiferromagnetic
Heisenberg chain in magnetic fields. It comes from string solutions which
continuously connect the mode of the lowest-energy excitations in the
zero-field limit and that of bound states of overturned spins from the
ferromagnetic state near the saturation field. We confirm the relevance to real
materials through comparisons with experimental results.
