  Let $G$ be an infinite countable discrete amenable group. For any $G$-action
on a compact metric space $(X,\rho)$, it turns out that if the action has
positive topological entropy, then for any sequence $\{s_i\}_{i=1}^{+\infty}$
with pairwise distinct elements in $G$ there exists a Cantor subset $K$ of $X$
which is Li-Yorke chaotic along this sequence, that is, for any two distinct
points $x,y\in K$, one has \[\limsup_{i\to+\infty}\rho(s_i x,s_iy)>0,\
\text{and}\ \liminf_{i\to+\infty}\rho(s_ix,s_iy)=0.\]
