The existence of stable reversal domains in thin film strips is predicted. The background magnetization is assumed to lie in the plane of the film and to be oriented perpendicular to the strip. Magnetostatic forces, which tend to enlarge a domain, are balanced by a bias field oriented against the magnetization within the domain. The force function is given in the limit in which the film thickness is negligible compared to the other dimensions of the domain. The bias field margins determined by spontaneous nucleation at the low end, and vanishing domain width at the upper end, are estimated.