DP-coloring is a generalization of list coloring introduced recently by Dvo����k and Postle. We prove that for every $n$-vertex graph $G$ whose chromatic number $��(G)$ is "close" to $n$, the DP-chromatic number of $G$ equals $��(G)$. "Close" here means $��(G)\geq n-O(\sqrt{n})$, and we also show that this lower bound is best possible (up to the constant factor in front of $\sqrt{n}$), in contrast to the case of list coloring.

9 pages; v2: incorporated referees' comments