  We report experimental verification of the recently predicted collective
modes of spinons, stabilized by backscattering interaction, in a model quantum
spin chain material. We exploit the unique geometry of uniform
Dzyaloshinskii-Moriya interactions in K$_2$CuSO$_4$Br$_2$ to measure the
interaction-induced splitting between the two components of the electron spin
resonance (ESR) response doublet. From that we directly determine the magnitude
of the "marginally irrelevant" backscattering interaction between spinons for
the first time.
