A new method is applied to study the steady motion and shape of a bubble in a channel in a Hele-Shaw cell. The procedure is based on a representation for the solution in terms of the Schwarz function S of the analytic curve that defines the interface separating the bubble from the viscous fluid. The problem is thereby reduced to the determination of the analytic function S. Interfacial tension effects are readily included in the formulation, though only when they are negligible is the solution obtained here. The resulting formulas agree with, but seem simpler than, those given about 30 years ago by Taylor and Saffinan, who used a different approach; in particular, it is shown that the two-parameter family of interface curves is a one-parameter family plus simple scale changes in the spatial coordinates. It is anticipated that the new approach may aid in the analysis of more difficult problems in which interfacial tension cannot be neglected.