  We report the observation of a frequency shift and splitting of the electron
spin resonance (ESR) mode of the low-dimensional S=1/2 frustrated
antiferromagnet Cs2CuCl4 in the spin-correlated state below the Curie-Weiss
temperature 4 K but above the ordering temperature 0.62 K. The shift and
splitting exhibit strong anisotropy with respect to the direction of the
applied magnetic field and do not vanish in zero field. The low-temperature
evolution of spin resonance response is a result of the specific modification
of one-dimensional spinon continuum under the action of the uniform
Dzyaloshinskii-Moriya interaction (DM) within the spin chains. Parameters of
the uniform DM interaction are derived from the experiment.
