  Li-Yorke chaos is a popular and well-studied notion of chaos. Several simple
and useful characterizations of this notion of chaos in the setting of linear
dynamics were obtained recently. In this note we show that even simpler and
more useful characterizations of Li-Yorke chaos can be given in the special
setting of composition operators on $L^p$ spaces. As a consequence we obtain a
simple characterization of weighted shifts which are Li-Yorke chaotic. We give
numerous examples to show that our results are sharp.
