A simple model is proposed to describe crazing in a very thin polymer film. It is argued that if the thickness of the film is below a certain critical value, the craze microstructure becomes similar to the deformation zone (two-dimensional neck) with the superimposed fibril structure. Deformation zone profile, characteristic fibril size, draw ratio, and critical film thickness are calculated as functions of material parameters and imposed strain rate. The results obtained are in good agreement with experimental values. The predictions of the model can also be used to verify the model of crazing in thick films and bulk polymers, which is described in Part 2 of the present series.