The viscoelastic behavior of entangled solutions of semiflexible chains is discussed. After identifying the different possible regimes of concentration and chain length in such a solution attention is focused on a "tightly-entangled" regime in which the polymer is confined to a tube of diameter less than its persistence length. A tube model analogous to the Doi-Edwards model is introduced to describe this regime. A general expression for the stress tensor of a solution of wormlike chains is derived, which may be applied to any concentration regime, and three intramolecular stress contributions are identified: a curvature contribution arising from forces that oppose transverse deformation or rotation of chain segments, a tension contribution arising from tangential forces that resist stretching or compression of the chain, and an orientational contribution that reduces in the appropriate limit to the Brownian stress of a rigid-rod solution. Intermolecular stress contributions are also calculated. A qualitative discussion is given of the high-frequency viscoelastic response of any solution of wormlike chains, which is dominated by the tension contribution and exhibits a characteristic power law dependence on frequency.