  Measurements of the magnetic susceptibility and its anisotropy in the
quasi-one-dimensional system o-TaS_{3} in its low-T charge density wave (CDW)
ground state are reported. Both sets of data reveal below 40 K an extra
paramagnetic contribution obeying a power-law temperature dependence
\chi(T)=AT^{-0.7}. The fact that the extra term measured previously in specific
heat in zero field, ascribed to low-energy CDW excitations, also follows a
power law C_{LEE}(0,T)=CT^{0.3}, strongly revives the case of random exchange
spin chains. Introduced impurities (0.5% Nb) only increase the amplitude C, but
do not change essentially the exponent. Within the two-level system (TLS)
model, we estimate from the amplitudes A and C that there is one TLS with a
spin s=1/2 localized on the chain at the lattice site per cca 900 Ta atoms. We
discuss the possibility that it is the charge frozen within a soliton-network
below the glass transition T_{g}~40 K determined recently in this system.
