The governing equations of monodomain isothermal cholesteric liquid crystals subjected to small amplitude oscillatory rectilinear shear have been derived for three representative helix orientations. The imposition of oscillatory flow excites splay-bend-twist deformations when the helix is aligned along the flow direction, splay-bend deformations when the helix is along the vorticity gradient, and twist deformations when aligned along the velocity axis. The different nature of the excited elastic modes as well as the anisotropic viscosities are reflected in the anisotropy of the linear viscoelastic material functions for small amplitude rectilinear oscillatory shear. When the helix is aligned along the flow direction, cholesteric viscoelasticity is strongest, and exists in a relatively narrow band of intermediate frequencies. When the helix is aligned along the vorticity direction cholesteric viscoelasticity is significant in a relatively broad range of intermediate frequencies. Finally, when the helix is aligned along the velocity gradient direction, cholesteric viscoelasticity is relatively insignificant and only exists in a narrow band of frequencies. The cholesteric pitch controls the location of viscoelastic region on the frequency spectrum, but only when the helix is not oriented along the vorticity axis.