Chromatic polynomial, which encodes the number of distinct ways to color the vertices of a graph, was introduced by George David Birkhoff in 1912 in attempt to attack the four-color problem. Motivated by the work of Khovanov, Helme-Guizon and Rong introduced a categorification of the chromatic polynomial. In this talk, I will give a brief introduction to this construction. If time permits, I will discuss how to define a categorification of signed chromatic polynomial. This is a joint work with Ziyi Lei, Yitian Wang and Yanguo Zhang.