For a proper vertex coloring c of a graph G, let φc(G) denote the maximum, over all induced subgraphs H of G, the difference between the chromatic number χ(H) and the number of colors used by c to color H. We define the chromatic discrepancy of a graph G, denoted by φ(G), to be the minimum φc(G), over all proper colorings c of G. If H is restricted to only connected induced subgraphs, we denote the corresponding parameter by φ(G). These parameters are aimed at studying graph colorings that use as few colors as possible in a graph and all its induced subgraphs. We study the parameters φ(G) and φ(G) and obtain bounds on them. We obtain general bounds, as well as bounds for certain special classes of graphs including random graphs. We provide structural characterizations of graphs with φ(G)=0 and graphs with φ(G)=0. We also show that computing these parameters is NP-hard. © 2014 Elsevier B.V. All rights reserved.