We propose a theory for the zero-shear viscosity of a dilute solution of wormlike micelles, with a length distribution as derived by Israelachvili, Mitchell, and Ninham. An analytical approach using Bohdanecky’s approximation to the full Yamakawa-Fujii-Yoshizaki description (YFY) for the viscosity of wormlike objects is combined with a numerical integration of the YFY equations. In principle, this provides a convenient means of extracting the growth parameters, dimensions, and persistence length of linear micelles from measurements of the viscosity as a function of the surfactant concentration.