The self-diffusion of fluorescently tagged poly(gamma-benzyl-alpha,L-glutamate), a helical, semiflexible synthetic homopolypeptide, has been measured in isotropic and cholesteric liquid-crystalline solutions by pattern fluorescence photobleaching recovery. On the isotropic side of the sharp isotropic-liquid-crystalline (ISO-LC) phase boundary, the rodlike polymers assume all possible orientations in a three-dimensional space, becoming enmeshed. In liquid-crystalline solutions, as first shown by Robinson [Trans. Faraday Soc. 52, 571 (1956)], spontaneous alignment of the cholesteric screw axis parallel to the optical (z) axis of the instrument produces small monodomains in which parallel rodlike polymers are organized into planes. Each horizontal plane is twisted slightly compared to its neighbors. Over the thickness of the sample, the rodlike polymers assume all possible orientations in this two-dimensional space. Despite the small size of the monodomains, it was possible to determine the self-diffusion coefficient of the semiflexible rods, orientationally averaged in two dimensions. Crossing the sharp ISO-LC phase boundary corresponds to the sudden release of any putative topological constraints active in the isotropic phase, and produced a modest but significant increase in diffusion. A relationship developed by Hess, Frenkel, and Allen [Mol. Phys. 74, 765 (1991)] is used to show that diffusion perpendicular to the rod axis is about ten times slower than diffusion parallel to the rod axis in the liquid-crystalline phase. In dilute solution, the comparable number would be 2. The perpendicular diffusion had decreased to about 8% of its initial value in dilute, isotropic solution. The parallel diffusion decreased to about 40% of its initial value. These results were obtained by neglecting the uncertain effects of semiflexibility. Likewise, the effects of modest polydispersity have not been treated explicitly.