  In this paper we study left 3-Engel elements in groups. In particular, we
prove that for any prime $p$ and any left 3-Engel element $x$ of finite
$p$-power order in a group $G$, $x^p$ is in the Baer radical of $G$. Also it is
proved that $<x,y>$ is nilpotent of class 4 for every two left 3-Engel elements
in a group $G$.
