  It is already known that the automorphism group of a chiral polyhedron is
never isomorphic to $PSL(2,q)$ or $PGL(2,q)$ for any prime power $q$. In this
paper, we show that $PSL(2,q)$ and $PGL(2,q)$ are never automorphism groups of
chiral polytopes of rank at least $5$. Moreover, we show that $PGL(2,q)$ is the
automorphism group of at least one chiral polytope of rank $4$ for every
$q\geq5$. Finally, we determine for which values of $q$ the group $PSL(2,q)$ is
the automorphism group of a chiral polytope of rank $4$, except when
$q=p^d\equiv3\pmod{4}$ where $d>1$ is not a prime power, in which case the
problem remains unsolved.
