  The angular and temperature dependences of single crystal ESR spectra at
X-band frequency of quasi 1D spin 1/2 antiferromagnetic zigzag chain system
{\beta}-TeVO4 are reported. Two resonance components in the ESR spectrum have
been detected: a weak narrow resonance on the top of the extremely broad
signal. The narrow line might be due to an impurity, the characteristics of the
broad absorption do not correlate with a picture of the typical behavior for
the V4+ ions (S = 1/2) with a square pyramidal environment. It was found that
at low temperatures the divergence of the spin susceptibility and linewidth of
the observed excitations can be due to a realization of three dimensional
magnetic ordering.
