  Assume that $G$ is a graph with edge ideal $I(G)$ and star packing number
$\alpha_2(G)$. We denote the $s$-th symbolic power of $I(G)$ by $I(G)^{(s)}$.
It is shown that the inequality ${\rm depth} S/(I(G)^{(s)})\geq
\alpha_2(G)-s+1$ is true for every chordal graph $G$ and every integer $s\geq
1$. Moreover, it is proved that for any graph $G$, we have ${\rm depth}
S/(I(G)^{(2)})\geq \alpha_2(G)-1$.
