  We report results of susceptibility chi and 7Li NMR measurements on LiVSi2O6.
The temperature dependence of the magnetic susceptibility chi(T) exhibits a
broad maximum, typical for low-dimensional magnetic systems. Quantitatively it
is in agreement with the expectation for an S=1 spin chain, represented by the
structural arrangement of V ions. The NMR results indicate antiferromagnetic
ordering below T_N=24 K. The intra- and interchain coupling J and J_p for
LiVSi2O6, and also for its sister compounds LiVGe2O6, NaVSi2O6 and NaVGe2O6,
are obtained via a modified random phase approximation which takes into account
results of quantum Monte Carlo calculations. While J_p is almost constant
across the series, J varies by a factor of 5, decreasing with increasing
lattice constant along the chain direction. The comparison between experimental
and theoretical susceptibility data suggests the presence of an easy-axis
magnetic anisotropy, which explains the formation of an energy gap in the
magnetic excitation spectrum below T_N, indicated by the variation of the NMR
spin-lattice relaxation rate at T << T_N.
