Constructions of Chiral Polytopes of Small Rank An abstract polytope of rank $n$ is said to be chiral if its automorphism group has precisely two orbits on the flags, such that adjacent flags belong to distinct orbits. This paper describes a general method for deriving new finite chiral polytopes from old finite chiral polytopes of the same rank. In particular, the technique is used to construct many new examples in ranks $3$, $4$, and $5$. Keywords:abstract regular polytope, chiral polytope, chiral mapsCategories:51M20, 52B15, 05C25