  The high-field ground state of the competing-spin-chain compound Cs2Cu2Mo3O12
with the ferromagnetic first-nearest-neighbor J1=-93 K and the
antiferromagnetic second-nearest-neighbor J2 = +33 K was investigated by
133Cs-NMR. A divergence of T1-1 and a peak-splitting in spectra were observed
at TN = 1.85 K, indicating the existence of a field-induced long range magnetic
order. In the paramagnetic region above 4 K, T1-1 showed a power-law
temperature dependence T2K-1. The exponent K was strongly field-dependent,
suggesting the possibility of the spin-nematic Tomonaga Luttinger Liquid state.
