A theory was developed for the steady-state extension of a wormlike chain, such as DNA, in flowing liquid with one end of the molecule tethered to a fixed object. This relates to recent experiments with individually imaged DNA molecules by Perkins, Smith, Larson, and Chu. The theory is based on the familiar Oseen tensor (also called Stokeslet) formalism of chain-molecule hydrodynamics applied to a bead-segment model. With the steady-state condition a normal-mode analysis is not necessary. The calculations are carried almost to the completely stretched state at high now rates, and reproduce the experiments well with a persistence length of 49.3 nm for the stained DNA. Measurements of extension of tethered single molecules in now analyzed by the method described here seem to make an excellent method for determining the persistence length of individual molecules.