A method is presented for calculating potential flows in infinite channels. Given a collection of N sources in the channel and a zero normal flow boundary condition, the method requires an amount of work proportional to N to evaluate the induced velocity field at each source position. It is accurate to within machine precision and for its performance does not depend on the distribution of the sources. Like the Fast Multipole Method developed by Greengard and Rokhlin [J. Comput. Phys., 73 (1987), pp. 325–348], it is based on a recursive subdivision of space, knowledge of the governing Green's function, and the use of asymptotic representations of the potential field. Previous schemes have been based either on conformal mapping, which experiences numerical difficulties with the domain boundary, or direct evaluation of Green's function. Both require $O(N^2 )$ work.