  In a class of three-dimensional abelian gauge theory the Lorentz invariance
is spontaneously broken by dynamical generation of a magnetic field. An
originally topologically massive photon becomes gapless, i.e. p_0=0 at {\vec
p}=0. Indeed, the photon is the Nambu-Goldstone boson associated with the
spontaneous breaking of the Lorentz invariance. Although symmetry generated by
two Lorentz boost generators is broken, there seems to appear only one physical
Nambu-Goldstone boson, namely a photon. We argue that the Ward identities in
the Nambu-Goldstone theorem are saturated by the photon pole.
