Given a polytope P, the Chvatal-Gomory procedure computes iteratively the integer hull PI of P. The Chvatal Rank of P is the minimal number of iterations needed to obtain PI. It is always finite, but already the rank of polytopes in R^2 can be arbitrarily large. We show that the Chvatal Rank of Polytopes in the 0/1 cube, which are of particular interest in combinatorial optimization, is at most 6n^3 log n, where n is the dimension of the cube. In the proof we use only elementary geometry and elementary number theory.