  A demonstration of how the point symmetries of the Chazy Equation become
nonlocal symmetries for the reduced equation is discussed. Moreover we
construct an equivalent third-order differential equation which is related to
the Chazy Equation under a generalized transformation, and find the point
symmetries of the Chazy Equation are generalized symmetries for the new
equation. With the use of singularity analysis and a simple coordinate
transformation we construct a solution for the Chazy Equation which is given by
a Right Painlev\'e Series. The singularity analysis is applied to the new
third-order equation and we find that it admits two solutions, one given by a
Left Painlev\'e Series and one given by a Right Painlev\'e Series where the
leading-order behaviors and the resonances are explicitly those of the Chazy
Equation.
