In this paper, we consider a continuous map $f:X\to X$ , 
where $X$ is a compact metric space , and discuss the 
existence of chaotic set of $f$, specially (as $X$=[0,1] ) . 
We prove that $f$ has a positively topological entropy 
if and only if it has an uncountably chaotic set in which 
each point is weakly almost periodic and is not almost periodic.