The intrinsic viscosity of the wormlike 3-arm star chain is evaluated in the Kirkwood-Riseman approximation by the use of the touched-bead hydrodynamic model. An interpolation formula is constructed for the mean reciprocal of the end-to-end distance of the once-broken wormlike chain which is necessary for the evaluation. A comparison is made of the present results with previous ones obtained by Monte Carlo simulations.