The disadvantage factor of a two-region slab lattice has been calculated using Case's formalism in one-velocity transport theory. Although the problem has not been solved exactly, the Fredholm equations for the expansion coefficients which are derived converge extremely rapidly under iteration. For the numerical calculations, an IBM-7090 code based on the results has been written; the disadvantage factor can be calculated with this code in two seconds. The problem treated in this paper is highly idealized, but Case's formalism admits extensions and may lead to efficient means of calculating disadvantage factors for more realistic models; some of the extensions will be given in a later paper.