Recently the study of finite permutation groups of rank 3 has received much attention. No doubt this is due to the fact that the new simple groups of Higman and Sims, McLaughlin, and Suzuki were constructed as rank 3 extensions of known permutation groups. Rank 3 extensions of multiply transitive groups have also been carefully studied. Tsuzuki [ 1 l] studied rank 3 extensions of S, , the symmetric group on n letters. Montague [S] classified the rank 3 extensions of PSI.,(q), PSU,(q), Sz(q), Ii(q), and A, . This paper is concerned with the rank 3 extensions of Frobenius groups. The analogous problem for doubly transitive groups is the classification of all transitive extensions of Frobenius groups, or equivalently the determination of all Zassenhaus groups which are not sharply doubly transitive. The problem for rank 3 groups is much easier than the classification of Zassenhaus groups, This is due to the fact that only a small number of groups occur. The main result of this paper is the following theorem.