  A $^{125}$Te nuclear magnetic resonance (NMR) study was carried out in the
paramagnetic state of the recently discovered quasi-one-dimensional spin-1
chain compound NiTe$_2$O$_5$. We observed that the $^{125}$Te NMR spectrum
splits into two in a magnetic field applied along the $c$ axis. Based on the
strong temperature variation of the relative intensity ratio of the split
lines, we infer that the line splitting arises from the two sublattice
susceptibilities induced in opposite directions along the chains. In great
support of this interpretation, a quantitative analysis of the spin-lattice
relaxation rate $T_1^{-1}$ and the Knight shift data unravels dominant
transverse spin fluctuations. We conclude that Ising-like uniaxial spin
correlations persist up to surprisingly high temperatures compared to the
exchange energy scales. Spin-charge coupling mechanism via a self-doping effect
may be important.
