A suitable cross section incorporating material anisotropy is shown to give circular birefringence in a slowly spun monomode fiber. It is assumed that the fractional variation Deltan/n of the refractive index satisfies the weak guidance condition Deltan/n << 1 and that the period (or pitch) p of the spun fiber is large enough so that the fundamental modes remain effectively bound. Under these assumptions the magnitude of the circular birefringence can be calculated from solutions of the scalar wave equation and in any case lies between the limits (0, 4pi/p). The value is zero in the absence of material anisotropy. The required material anisotropy could be produced by stress implanted in the core.