A class of hierarchically chiral metamaterials was analyzed with the finite element method for their effective linear viscoelastic properties under low frequency, uniaxial straining. The viscoelastic property of the solid phase was assumed to be of the standard linear solid. It is found that from Rank-1 to Rank-2 hierarchy effective Young’s modulus is enhanced. From Rank-2 to Rank-3, effective modulus may be roughly the same, slightly increased or decreased, depending on the ligament thickness. When the ligament thickness is less than 1.5 mm, increasing hierarchy decreases the overall damping. For larger thickness, overall damping may be slightly enhanced by hierarchy. Gradient lateral deformation is observed in the metamaterials under uniaxial straining, indicating the existence of chiral effects.