  We study a model which could explain some of the unusual magnetic properties
observed for the one-dimensional helical spin system Co(hfac)_2 NITPhOMe. One
of the properties observed is that the magnetization shows plateaus near zero
and near one-third of the saturation value if a magnetic field is applied along
the helical axis, but not if the field is applied in the plane perpendicular to
that axis. The system consists of a spin-1/2 chain in which cobalt ions (which
are highly anisotropic with an easy axis e_i) and organic radicals (which are
isotropic) alternate with each other. The easy axis of the cobalts e_i lie at
an angle theta_i with respect to the helical axis, while the projection of
e_{i+1} - e_i on the plane perpendicular to the helical axis is given by 2 pi
/3. For temperatures and magnetic fields which are much smaller than the
coupling between the nearest-neighbor cobalts and radicals, one can integrate
out the radicals to obtain an Ising model for the cobalts; this enables one to
compute the thermodynamic properties of the system using the transfer matrix
approach. We consider a model in which the tilt angles theta_i are allowed to
vary with i with period three; we find that for certain patterns of theta_i,
the system shows the magnetization plateaus mentioned above. At the ends of the
plateaus, the entropy is finite even at very low temperatures, while the
magnetic susceptibility and specific heat also show some interesting features.
