  The Leggett mode associated with out-of-phase oscillations of superconducting
phase in multi-band superconductors usually is heavy due to the interband
coupling, which makes its excitation and detection difficult. We report on the
existence of a massless Leggett mode in three-band superconductors with
time-reversal-symmetry-breaking (TRSB). The mass of the Leggett mode is small
close to the TRSB transition and vanishes at the transition point, and thus
locates within the smallest superconducting energy gap, which makes it stable
and detectable. The mass of the Leggett mode can be measured by Raman
spectroscopy. The thermodynamic consequences of this massless mode and possible
realization in iron-based superconductors are also discussed.
