A "breather excitation" is observed directly by electron spin resonance in the quantum spin chain Cu benzoate, in which an unexpected field-induced gap has recently been found. The nonlinear field dependence of the resonance field agrees well with the formula based on a quantum sine-Gordon model. The power-law temperature dependence of the linewidth is observed in the gapless spinon regime while the width decreases exponentially for the gapped breather regime. In the intermediate range, a distinct anomaly is found, which is the manifestation of "the spinon-breather dynamical crossover."